first commit

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/common_tests.py

@@ -0,0 +1,337 @@
+import pickle
+
+import numpy as np
+import numpy.testing as npt
+from numpy.testing import assert_allclose, assert_equal
+from pytest import raises as assert_raises
+
+import numpy.ma.testutils as ma_npt
+
+from scipy._lib._util import getfullargspec_no_self as _getfullargspec
+from scipy import stats
+
+
+def check_named_results(res, attributes, ma=False):
+    for i, attr in enumerate(attributes):
+        if ma:
+            ma_npt.assert_equal(res[i], getattr(res, attr))
+        else:
+            npt.assert_equal(res[i], getattr(res, attr))
+
+
+def check_normalization(distfn, args, distname):
+    norm_moment = distfn.moment(0, *args)
+    npt.assert_allclose(norm_moment, 1.0)
+
+    # this is a temporary plug: either ncf or expect is problematic;
+    # best be marked as a knownfail, but I've no clue how to do it.
+    if distname == "ncf":
+        atol, rtol = 1e-5, 0
+    else:
+        atol, rtol = 1e-7, 1e-7
+
+    normalization_expect = distfn.expect(lambda x: 1, args=args)
+    npt.assert_allclose(normalization_expect, 1.0, atol=atol, rtol=rtol,
+            err_msg=distname, verbose=True)
+
+    _a, _b = distfn.support(*args)
+    normalization_cdf = distfn.cdf(_b, *args)
+    npt.assert_allclose(normalization_cdf, 1.0)
+
+
+def check_moment(distfn, arg, m, v, msg):
+    m1 = distfn.moment(1, *arg)
+    m2 = distfn.moment(2, *arg)
+    if not np.isinf(m):
+        npt.assert_almost_equal(m1, m, decimal=10, err_msg=msg +
+                            ' - 1st moment')
+    else:                     # or np.isnan(m1),
+        npt.assert_(np.isinf(m1),
+               msg + ' - 1st moment -infinite, m1=%s' % str(m1))
+
+    if not np.isinf(v):
+        npt.assert_almost_equal(m2 - m1 * m1, v, decimal=10, err_msg=msg +
+                            ' - 2ndt moment')
+    else:                     # or np.isnan(m2),
+        npt.assert_(np.isinf(m2),
+               msg + ' - 2nd moment -infinite, m2=%s' % str(m2))
+
+
+def check_mean_expect(distfn, arg, m, msg):
+    if np.isfinite(m):
+        m1 = distfn.expect(lambda x: x, arg)
+        npt.assert_almost_equal(m1, m, decimal=5, err_msg=msg +
+                            ' - 1st moment (expect)')
+
+
+def check_var_expect(distfn, arg, m, v, msg):
+    if np.isfinite(v):
+        m2 = distfn.expect(lambda x: x*x, arg)
+        npt.assert_almost_equal(m2, v + m*m, decimal=5, err_msg=msg +
+                            ' - 2st moment (expect)')
+
+
+def check_skew_expect(distfn, arg, m, v, s, msg):
+    if np.isfinite(s):
+        m3e = distfn.expect(lambda x: np.power(x-m, 3), arg)
+        npt.assert_almost_equal(m3e, s * np.power(v, 1.5),
+                decimal=5, err_msg=msg + ' - skew')
+    else:
+        npt.assert_(np.isnan(s))
+
+
+def check_kurt_expect(distfn, arg, m, v, k, msg):
+    if np.isfinite(k):
+        m4e = distfn.expect(lambda x: np.power(x-m, 4), arg)
+        npt.assert_allclose(m4e, (k + 3.) * np.power(v, 2), atol=1e-5, rtol=1e-5,
+                err_msg=msg + ' - kurtosis')
+    elif not np.isposinf(k):
+        npt.assert_(np.isnan(k))
+
+
+def check_entropy(distfn, arg, msg):
+    ent = distfn.entropy(*arg)
+    npt.assert_(not np.isnan(ent), msg + 'test Entropy is nan')
+
+
+def check_private_entropy(distfn, args, superclass):
+    # compare a generic _entropy with the distribution-specific implementation
+    npt.assert_allclose(distfn._entropy(*args),
+                        superclass._entropy(distfn, *args))
+
+
+def check_entropy_vect_scale(distfn, arg):
+    # check 2-d
+    sc = np.asarray([[1, 2], [3, 4]])
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc.ravel()]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+    # check invalid value, check cast
+    sc = [1, 2, -3]
+    v_ent = distfn.entropy(*arg, scale=sc)
+    s_ent = [distfn.entropy(*arg, scale=s) for s in sc]
+    s_ent = np.asarray(s_ent).reshape(v_ent.shape)
+    assert_allclose(v_ent, s_ent, atol=1e-14)
+
+
+def check_edge_support(distfn, args):
+    # Make sure that x=self.a and self.b are handled correctly.
+    x = distfn.support(*args)
+    if isinstance(distfn, stats.rv_discrete):
+        x = x[0]-1, x[1]
+
+    npt.assert_equal(distfn.cdf(x, *args), [0.0, 1.0])
+    npt.assert_equal(distfn.sf(x, *args), [1.0, 0.0])
+
+    if distfn.name not in ('skellam', 'dlaplace'):
+        # with a = -inf, log(0) generates warnings
+        npt.assert_equal(distfn.logcdf(x, *args), [-np.inf, 0.0])
+        npt.assert_equal(distfn.logsf(x, *args), [0.0, -np.inf])
+
+    npt.assert_equal(distfn.ppf([0.0, 1.0], *args), x)
+    npt.assert_equal(distfn.isf([0.0, 1.0], *args), x[::-1])
+
+    # out-of-bounds for isf & ppf
+    npt.assert_(np.isnan(distfn.isf([-1, 2], *args)).all())
+    npt.assert_(np.isnan(distfn.ppf([-1, 2], *args)).all())
+
+
+def check_named_args(distfn, x, shape_args, defaults, meths):
+    ## Check calling w/ named arguments.
+
+    # check consistency of shapes, numargs and _parse signature
+    signature = _getfullargspec(distfn._parse_args)
+    npt.assert_(signature.varargs is None)
+    npt.assert_(signature.varkw is None)
+    npt.assert_(not signature.kwonlyargs)
+    npt.assert_(list(signature.defaults) == list(defaults))
+
+    shape_argnames = signature.args[:-len(defaults)]  # a, b, loc=0, scale=1
+    if distfn.shapes:
+        shapes_ = distfn.shapes.replace(',', ' ').split()
+    else:
+        shapes_ = ''
+    npt.assert_(len(shapes_) == distfn.numargs)
+    npt.assert_(len(shapes_) == len(shape_argnames))
+
+    # check calling w/ named arguments
+    shape_args = list(shape_args)
+
+    vals = [meth(x, *shape_args) for meth in meths]
+    npt.assert_(np.all(np.isfinite(vals)))
+
+    names, a, k = shape_argnames[:], shape_args[:], {}
+    while names:
+        k.update({names.pop(): a.pop()})
+        v = [meth(x, *a, **k) for meth in meths]
+        npt.assert_array_equal(vals, v)
+        if 'n' not in k.keys():
+            # `n` is first parameter of moment(), so can't be used as named arg
+            npt.assert_equal(distfn.moment(1, *a, **k),
+                             distfn.moment(1, *shape_args))
+
+    # unknown arguments should not go through:
+    k.update({'kaboom': 42})
+    assert_raises(TypeError, distfn.cdf, x, **k)
+
+
+def check_random_state_property(distfn, args):
+    # check the random_state attribute of a distribution *instance*
+
+    # This test fiddles with distfn.random_state. This breaks other tests,
+    # hence need to save it and then restore.
+    rndm = distfn.random_state
+
+    # baseline: this relies on the global state
+    np.random.seed(1234)
+    distfn.random_state = None
+    r0 = distfn.rvs(*args, size=8)
+
+    # use an explicit instance-level random_state
+    distfn.random_state = 1234
+    r1 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    distfn.random_state = np.random.RandomState(1234)
+    r2 = distfn.rvs(*args, size=8)
+    npt.assert_equal(r0, r2)
+
+    # check that np.random.Generator can be used (numpy >= 1.17)
+    if hasattr(np.random, 'default_rng'):
+        # obtain a np.random.Generator object
+        rng = np.random.default_rng(1234)
+        distfn.rvs(*args, size=1, random_state=rng)
+
+    # can override the instance-level random_state for an individual .rvs call
+    distfn.random_state = 2
+    orig_state = distfn.random_state.get_state()
+
+    r3 = distfn.rvs(*args, size=8, random_state=np.random.RandomState(1234))
+    npt.assert_equal(r0, r3)
+
+    # ... and that does not alter the instance-level random_state!
+    npt.assert_equal(distfn.random_state.get_state(), orig_state)
+
+    # finally, restore the random_state
+    distfn.random_state = rndm
+
+
+def check_meth_dtype(distfn, arg, meths):
+    q0 = [0.25, 0.5, 0.75]
+    x0 = distfn.ppf(q0, *arg)
+    x_cast = [x0.astype(tp) for tp in
+                        (np.int_, np.float16, np.float32, np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+        for meth in meths:
+            val = meth(x, *arg)
+            npt.assert_(val.dtype == np.float_)
+
+
+def check_ppf_dtype(distfn, arg):
+    q0 = np.asarray([0.25, 0.5, 0.75])
+    q_cast = [q0.astype(tp) for tp in (np.float16, np.float32, np.float64)]
+    for q in q_cast:
+        for meth in [distfn.ppf, distfn.isf]:
+            val = meth(q, *arg)
+            npt.assert_(val.dtype == np.float_)
+
+
+def check_cmplx_deriv(distfn, arg):
+    # Distributions allow complex arguments.
+    def deriv(f, x, *arg):
+        x = np.asarray(x)
+        h = 1e-10
+        return (f(x + h*1j, *arg)/h).imag
+
+    x0 = distfn.ppf([0.25, 0.51, 0.75], *arg)
+    x_cast = [x0.astype(tp) for tp in
+                        (np.int_, np.float16, np.float32, np.float64)]
+
+    for x in x_cast:
+        # casting may have clipped the values, exclude those
+        distfn._argcheck(*arg)
+        x = x[(distfn.a < x) & (x < distfn.b)]
+
+        pdf, cdf, sf = distfn.pdf(x, *arg), distfn.cdf(x, *arg), distfn.sf(x, *arg)
+        assert_allclose(deriv(distfn.cdf, x, *arg), pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logcdf, x, *arg), pdf/cdf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.sf, x, *arg), -pdf, rtol=1e-5)
+        assert_allclose(deriv(distfn.logsf, x, *arg), -pdf/sf, rtol=1e-5)
+
+        assert_allclose(deriv(distfn.logpdf, x, *arg),
+                        deriv(distfn.pdf, x, *arg) / distfn.pdf(x, *arg),
+                        rtol=1e-5)
+
+
+def check_pickling(distfn, args):
+    # check that a distribution instance pickles and unpickles
+    # pay special attention to the random_state property
+
+    # save the random_state (restore later)
+    rndm = distfn.random_state
+
+    # check unfrozen
+    distfn.random_state = 1234
+    distfn.rvs(*args, size=8)
+    s = pickle.dumps(distfn)
+    r0 = distfn.rvs(*args, size=8)
+
+    unpickled = pickle.loads(s)
+    r1 = unpickled.rvs(*args, size=8)
+    npt.assert_equal(r0, r1)
+
+    # also smoke test some methods
+    medians = [distfn.ppf(0.5, *args), unpickled.ppf(0.5, *args)]
+    npt.assert_equal(medians[0], medians[1])
+    npt.assert_equal(distfn.cdf(medians[0], *args),
+                     unpickled.cdf(medians[1], *args))
+
+    # check frozen pickling/unpickling with rvs
+    frozen_dist = distfn(*args)
+    pkl = pickle.dumps(frozen_dist)
+    unpickled = pickle.loads(pkl)
+
+    r0 = frozen_dist.rvs(size=8)
+    r1 = unpickled.rvs(size=8)
+    npt.assert_equal(r0, r1)
+
+    # check pickling/unpickling of .fit method
+    if hasattr(distfn, "fit"):
+        fit_function = distfn.fit
+        pickled_fit_function = pickle.dumps(fit_function)
+        unpickled_fit_function = pickle.loads(pickled_fit_function)
+        assert fit_function.__name__ == unpickled_fit_function.__name__ == "fit"
+    
+    # restore the random_state
+    distfn.random_state = rndm
+
+
+def check_freezing(distfn, args):
+    # regression test for gh-11089: freezing a distribution fails
+    # if loc and/or scale are specified
+    if isinstance(distfn, stats.rv_continuous):
+        locscale = {'loc': 1, 'scale': 2}
+    else:
+        locscale = {'loc': 1}
+
+    rv = distfn(*args, **locscale)
+    assert rv.a == distfn(*args).a
+    assert rv.b == distfn(*args).b
+
+
+def check_rvs_broadcast(distfunc, distname, allargs, shape, shape_only, otype):
+    np.random.seed(123)
+    sample = distfunc.rvs(*allargs)
+    assert_equal(sample.shape, shape, "%s: rvs failed to broadcast" % distname)
+    if not shape_only:
+        rvs = np.vectorize(lambda *allargs: distfunc.rvs(*allargs), otypes=otype)
+        np.random.seed(123)
+        expected = rvs(*allargs)
+        assert_allclose(sample, expected, rtol=1e-13)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/data/nist_anova/AtmWtAg.dat

@@ -0,0 +1,108 @@
+NIST/ITL StRD 
+Dataset Name:   AtmWtAg   (AtmWtAg.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 108) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Powell, L.J., Murphy, T.J. and Gramlich, J.W. (1982).
+                "The Absolute Isotopic Abundance & Atomic Weight
+                of a Reference Sample of Silver".
+                NBS Journal of Research, 87, pp. 9-19.
+
+
+Data:           1 Factor
+                2 Treatments
+                24 Replicates/Cell
+                48 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Observed Data
+
+
+Model:          3 Parameters (mu, tau_1, tau_2)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+
+Between Instrument  1 3.63834187500000E-09 3.63834187500000E-09 1.59467335677930E+01
+Within Instrument  46 1.04951729166667E-08 2.28155932971014E-10
+
+                   Certified R-Squared 2.57426544538321E-01
+
+                   Certified Residual
+                   Standard Deviation  1.51048314446410E-05
+
+
+
+
+
+
+
+
+
+
+
+Data:  Instrument           AgWt
+           1            107.8681568
+           1            107.8681465
+           1            107.8681572
+           1            107.8681785
+           1            107.8681446
+           1            107.8681903
+           1            107.8681526
+           1            107.8681494
+           1            107.8681616
+           1            107.8681587
+           1            107.8681519
+           1            107.8681486
+           1            107.8681419
+           1            107.8681569
+           1            107.8681508
+           1            107.8681672
+           1            107.8681385
+           1            107.8681518
+           1            107.8681662
+           1            107.8681424
+           1            107.8681360
+           1            107.8681333
+           1            107.8681610
+           1            107.8681477
+           2            107.8681079
+           2            107.8681344
+           2            107.8681513
+           2            107.8681197
+           2            107.8681604
+           2            107.8681385
+           2            107.8681642
+           2            107.8681365
+           2            107.8681151
+           2            107.8681082
+           2            107.8681517
+           2            107.8681448
+           2            107.8681198
+           2            107.8681482
+           2            107.8681334
+           2            107.8681609
+           2            107.8681101
+           2            107.8681512
+           2            107.8681469
+           2            107.8681360
+           2            107.8681254
+           2            107.8681261
+           2            107.8681450
+           2            107.8681368

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/data/nist_anova/SiRstv.dat

@@ -0,0 +1,85 @@
+NIST/ITL StRD 
+Dataset Name:   SiRstv     (SiRstv.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 85) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Ehrstein, James and Croarkin, M. Carroll.
+                Unpublished NIST dataset.
+
+
+Data:           1 Factor
+                5 Treatments
+                5  Replicates/Cell
+                25 Observations
+                3 Constant Leading Digits
+                Lower Level of Difficulty
+                Observed Data
+
+
+Model:          6 Parameters (mu,tau_1, ... , tau_5)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Instrument  4 5.11462616000000E-02 1.27865654000000E-02 1.18046237440255E+00
+Within Instrument  20 2.16636560000000E-01 1.08318280000000E-02
+
+                   Certified R-Squared 1.90999039051129E-01
+
+                   Certified Residual
+                   Standard Deviation  1.04076068334656E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Instrument   Resistance
+           1         196.3052
+           1         196.1240
+           1         196.1890
+           1         196.2569
+           1         196.3403
+           2         196.3042
+           2         196.3825
+           2         196.1669
+           2         196.3257
+           2         196.0422
+           3         196.1303
+           3         196.2005
+           3         196.2889
+           3         196.0343
+           3         196.1811
+           4         196.2795
+           4         196.1748
+           4         196.1494
+           4         196.1485
+           4         195.9885
+           5         196.2119
+           5         196.1051
+           5         196.1850
+           5         196.0052
+           5         196.2090

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/data/nist_anova/SmLs01.dat

@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs01   (SmLs01.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                1 Constant Leading Digit
+                Lower Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1         1.4
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           1         1.3
+           1         1.5
+           2         1.3
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           2         1.2
+           2         1.4
+           3         1.5
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           3         1.4
+           3         1.6
+           4         1.3
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           4         1.2
+           4         1.4
+           5         1.5
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           5         1.4
+           5         1.6
+           6         1.3
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           6         1.2
+           6         1.4
+           7         1.5
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           7         1.4
+           7         1.6
+           8         1.3
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           8         1.2
+           8         1.4
+           9         1.5
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6
+           9         1.4
+           9         1.6

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/data/nist_anova/SmLs04.dat

@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs04   (SmLs04.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                7 Constant Leading Digits
+                Average Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares             F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1       1000000.4
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           1       1000000.3
+           1       1000000.5
+           2       1000000.3
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           2       1000000.2
+           2       1000000.4
+           3       1000000.5
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           3       1000000.4
+           3       1000000.6
+           4       1000000.3
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           4       1000000.2
+           4       1000000.4
+           5       1000000.5
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           5       1000000.4
+           5       1000000.6
+           6       1000000.3
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           6       1000000.2
+           6       1000000.4
+           7       1000000.5
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           7       1000000.4
+           7       1000000.6
+           8       1000000.3
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           8       1000000.2
+           8       1000000.4
+           9       1000000.5
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6
+           9       1000000.4
+           9       1000000.6

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/data/nist_anova/SmLs07.dat

@@ -0,0 +1,249 @@
+NIST/ITL StRD 
+Dataset Name:   SmLs07   (SmLs07.dat)
+
+
+File Format:    ASCII
+                Certified Values   (lines 41 to 47)
+                Data               (lines 61 to 249) 
+
+
+Procedure:      Analysis of Variance
+
+
+Reference:      Simon, Stephen D. and Lesage, James P. (1989).
+                "Assessing the Accuracy of ANOVA Calculations in
+                Statistical Software".
+                Computational Statistics & Data Analysis, 8, pp. 325-332.
+
+
+Data:           1 Factor
+                9 Treatments
+                21 Replicates/Cell
+                189 Observations
+                13 Constant Leading Digits
+                Higher Level of Difficulty
+                Generated Data
+
+
+Model:          10 Parameters (mu,tau_1, ... , tau_9)
+                y_{ij} = mu + tau_i + epsilon_{ij}
+
+
+
+
+
+
+Certified Values:
+
+Source of                  Sums of               Mean               
+Variation          df      Squares              Squares            F Statistic
+
+Between Treatment   8 1.68000000000000E+00 2.10000000000000E-01 2.10000000000000E+01
+Within Treatment  180 1.80000000000000E+00 1.00000000000000E-02
+
+                  Certified R-Squared 4.82758620689655E-01
+
+                  Certified Residual
+                  Standard Deviation  1.00000000000000E-01
+
+
+
+
+
+
+
+
+
+
+
+
+Data:  Treatment   Response
+           1    1000000000000.4
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           1    1000000000000.3
+           1    1000000000000.5
+           2    1000000000000.3
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           2    1000000000000.2
+           2    1000000000000.4
+           3    1000000000000.5
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           3    1000000000000.4
+           3    1000000000000.6
+           4    1000000000000.3
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           4    1000000000000.2
+           4    1000000000000.4
+           5    1000000000000.5
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           5    1000000000000.4
+           5    1000000000000.6
+           6    1000000000000.3
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           6    1000000000000.2
+           6    1000000000000.4
+           7    1000000000000.5
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           7    1000000000000.4
+           7    1000000000000.6
+           8    1000000000000.3
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           8    1000000000000.2
+           8    1000000000000.4
+           9    1000000000000.5
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6
+           9    1000000000000.4
+           9    1000000000000.6

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/data/nist_linregress/Norris.dat

@@ -0,0 +1,97 @@
+NIST/ITL StRD
+Dataset Name:  Norris (Norris.dat)
+
+File Format:   ASCII
+               Certified Values  (lines 31 to 46)
+               Data              (lines 61 to 96)
+
+Procedure:     Linear Least Squares Regression
+
+Reference:     Norris, J., NIST.  
+               Calibration of Ozone Monitors.
+
+Data:          1 Response Variable (y)
+               1 Predictor Variable (x)
+               36 Observations
+               Lower Level of Difficulty
+               Observed Data
+
+Model:         Linear Class
+               2 Parameters (B0,B1)
+
+               y = B0 + B1*x + e
+
+
+
+               Certified Regression Statistics
+
+                                          Standard Deviation
+     Parameter          Estimate             of Estimate
+
+        B0        -0.262323073774029     0.232818234301152
+        B1         1.00211681802045      0.429796848199937E-03
+
+     Residual
+     Standard Deviation   0.884796396144373
+
+     R-Squared            0.999993745883712
+
+
+               Certified Analysis of Variance Table
+
+Source of Degrees of    Sums of             Mean  
+Variation  Freedom      Squares            Squares           F Statistic
+              
+Regression    1     4255954.13232369   4255954.13232369   5436385.54079785
+Residual     34     26.6173985294224   0.782864662630069
+
+                 
+                                          
+                                          
+                                                           
+
+                            
+                                   
+                                                       
+
+
+
+
+Data:       y          x
+           0.1        0.2
+         338.8      337.4
+         118.1      118.2
+         888.0      884.6
+           9.2       10.1
+         228.1      226.5
+         668.5      666.3
+         998.5      996.3
+         449.1      448.6
+         778.9      777.0
+         559.2      558.2
+           0.3        0.4
+           0.1        0.6
+         778.1      775.5
+         668.8      666.9
+         339.3      338.0
+         448.9      447.5
+          10.8       11.6
+         557.7      556.0
+         228.3      228.1
+         998.0      995.8
+         888.8      887.6
+         119.6      120.2
+           0.3        0.3
+           0.6        0.3
+         557.6      556.8
+         339.3      339.1
+         888.0      887.2
+         998.5      999.0
+         778.9      779.0
+          10.2       11.1
+         117.6      118.3
+         228.9      229.2
+         668.4      669.1
+         449.2      448.9
+           0.2        0.5
+                                   

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/studentized_range_mpmath_ref.py

@@ -0,0 +1,252 @@
+# To run this script, run
+# `python studentized_range_mpmath_ref.py`
+# in the "scipy/stats/tests/" directory
+
+# This script generates a JSON file "./data/studentized_range_mpmath_ref.json"
+# that is used to compare the accuracy of `studentized_range` functions against
+# precise (20 DOP) results generated using `mpmath`.
+
+# Equations in this file have been taken from
+# https://en.wikipedia.org/wiki/Studentized_range_distribution
+# and have been checked against the following reference:
+# Lund, R. E., and J. R. Lund. "Algorithm AS 190: Probabilities and
+# Upper Quantiles for the Studentized Range." Journal of the Royal
+# Statistical Society. Series C (Applied Statistics), vol. 32, no. 2,
+# 1983, pp. 204-210. JSTOR, www.jstor.org/stable/2347300. Accessed 18
+# Feb. 2021.
+
+# Note: I would have prefered to use pickle rather than JSON, but -
+# due to security concerns - decided against it.
+import itertools
+from collections import namedtuple
+import json
+import time
+
+import os
+from multiprocessing import Pool, cpu_count
+
+from mpmath import gamma, pi, sqrt, quad, inf, mpf, mp
+from mpmath import npdf as phi
+from mpmath import ncdf as Phi
+
+results_filepath = "data/studentized_range_mpmath_ref.json"
+num_pools = max(cpu_count() - 1, 1)
+
+MPResult = namedtuple("MPResult", ["src_case", "mp_result"])
+
+CdfCase = namedtuple("CdfCase",
+                     ["q", "k", "v", "expected_atol", "expected_rtol"])
+
+MomentCase = namedtuple("MomentCase",
+                        ["m", "k", "v", "expected_atol", "expected_rtol"])
+
+# Load previously generated JSON results, or init a new dict if none exist
+if os.path.isfile(results_filepath):
+    res_dict = json.load(open(results_filepath, mode="r"))
+else:
+    res_dict = dict()
+
+# Frame out data structure. Store data with the function type as a top level
+# key to allow future expansion
+res_dict["COMMENT"] = ("!!!!!! THIS FILE WAS AUTOGENERATED BY RUNNING "
+                       "`python studentized_range_mpmath_ref.py` !!!!!!")
+res_dict.setdefault("cdf_data", [])
+res_dict.setdefault("pdf_data", [])
+res_dict.setdefault("moment_data", [])
+
+general_atol, general_rtol = 1e-11, 1e-11
+
+mp.dps = 24
+
+cp_q = [0.1, 1, 4, 10]
+cp_k = [3, 10, 20]
+cp_nu = [3, 10, 20, 50, 100, 120]
+
+cdf_pdf_cases = [
+    CdfCase(*case,
+            general_atol,
+            general_rtol)
+    for case in
+    itertools.product(cp_q, cp_k, cp_nu)
+]
+
+mom_atol, mom_rtol = 1e-9, 1e-9
+# These are EXTREMELY slow - Multiple days each in worst case.
+moment_cases = [
+    MomentCase(i, 3, 10, mom_atol, mom_rtol)
+    for i in range(5)
+]
+
+
+def write_data():
+    """Writes the current res_dict to the target JSON file"""
+    with open(results_filepath, mode="w") as f:
+        json.dump(res_dict, f, indent=2)
+
+
+def to_dict(named_tuple):
+    """Converts a namedtuple to a dict"""
+    return dict(named_tuple._asdict())
+
+
+def mp_res_to_dict(mp_result):
+    """Formats an MPResult namedtuple into a dict for JSON dumping"""
+    return {
+        "src_case": to_dict(mp_result.src_case),
+
+        # np assert can't handle mpf, so take the accuracy hit here.
+        "mp_result": float(mp_result.mp_result)
+    }
+
+
+def cdf_mp(q, k, nu):
+    """Straightforward implementation of studentized range CDF"""
+    q, k, nu = mpf(q), mpf(k), mpf(nu)
+
+    def inner(s, z):
+        return phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 1)
+
+    def outer(s, z):
+        return s ** (nu - 1) * phi(sqrt(nu) * s) * inner(s, z)
+
+    def whole(s, z):
+        return (sqrt(2 * pi) * k * nu ** (nu / 2)
+                / (gamma(nu / 2) * 2 ** (nu / 2 - 1)) * outer(s, z))
+
+    res = quad(whole, [0, inf], [-inf, inf],
+               method="gauss-legendre", maxdegree=10)
+    return res
+
+
+def pdf_mp(q, k, nu):
+    """Straightforward implementation of studentized range PDF"""
+    q, k, nu = mpf(q), mpf(k), mpf(nu)
+
+    def inner(s, z):
+        return phi(z + q * s) * phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 2)
+
+    def outer(s, z):
+        return s ** nu * phi(sqrt(nu) * s) * inner(s, z)
+
+    def whole(s, z):
+        return (sqrt(2 * pi) * k * (k - 1) * nu ** (nu / 2)
+                / (gamma(nu / 2) * 2 ** (nu / 2 - 1)) * outer(s, z))
+
+    res = quad(whole, [0, inf], [-inf, inf],
+               method="gauss-legendre", maxdegree=10)
+    return res
+
+
+def moment_mp(m, k, nu):
+    """Implementation of the studentized range moment"""
+    m, k, nu = mpf(m), mpf(k), mpf(nu)
+
+    def inner(q, s, z):
+        return phi(z + q * s) * phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 2)
+
+    def outer(q, s, z):
+        return s ** nu * phi(sqrt(nu) * s) * inner(q, s, z)
+
+    def pdf(q, s, z):
+        return (sqrt(2 * pi) * k * (k - 1) * nu ** (nu / 2)
+                / (gamma(nu / 2) * 2 ** (nu / 2 - 1)) * outer(q, s, z))
+
+    def whole(q, s, z):
+        return q ** m * pdf(q, s, z)
+
+    res = quad(whole, [0, inf], [0, inf], [-inf, inf],
+               method="gauss-legendre", maxdegree=10)
+    return res
+
+
+def result_exists(set_key, case):
+    """Searches the results dict for a result in the set that matches a case.
+    Returns True if such a case exists."""
+    if set_key not in res_dict:
+        raise ValueError(f"{set_key} not present in data structure!")
+
+    case_dict = to_dict(case)
+    existing_res = list(filter(
+        lambda res: res["src_case"] == case_dict,  # dict comparison
+        res_dict[set_key]))
+
+    return len(existing_res) > 0
+
+
+def run(case, run_lambda, set_key, index=0, total_cases=0):
+    """Runs the single passed case, returning an mp dictionary and index"""
+    t_start = time.perf_counter()
+
+    res = run_lambda(case)
+
+    print(f"Finished {index + 1}/{total_cases} in batch. "
+          f"(Took {time.perf_counter() - t_start}s)")
+
+    return index, set_key, mp_res_to_dict(MPResult(case, res))
+
+
+def write_result(res):
+    """A callback for completed jobs. Inserts and writes a calculated result
+     to file."""
+    index, set_key, result_dict = res
+    res_dict[set_key].insert(index, result_dict)
+    write_data()
+
+
+def run_cases(cases, run_lambda, set_key):
+    """Runs an array of cases and writes to file"""
+    # Generate jobs to run from cases that do not have a result in
+    # the previously loaded JSON.
+    job_arg = [(case, run_lambda, set_key, index, len(cases))
+               for index, case in enumerate(cases)
+               if not result_exists(set_key, case)]
+
+    print(f"{len(cases) - len(job_arg)}/{len(cases)} cases won't be "
+          f"calculated because their results already exist.")
+
+    jobs = []
+    pool = Pool(num_pools)
+
+    # Run all using multiprocess
+    for case in job_arg:
+        jobs.append(pool.apply_async(run, args=case, callback=write_result))
+
+    pool.close()
+    pool.join()
+
+
+def run_pdf(case):
+    return pdf_mp(case.q, case.k, case.v)
+
+
+def run_cdf(case):
+    return cdf_mp(case.q, case.k, case.v)
+
+
+def run_moment(case):
+    return moment_mp(case.m, case.k, case.v)
+
+
+def main():
+    t_start = time.perf_counter()
+
+    total_cases = 2 * len(cdf_pdf_cases) + len(moment_cases)
+    print(f"Processing {total_cases} test cases")
+
+    print(f"Running 1st batch ({len(cdf_pdf_cases)} PDF cases). "
+          f"These take about 30s each.")
+    run_cases(cdf_pdf_cases, run_pdf, "pdf_data")
+
+    print(f"Running 2nd batch ({len(cdf_pdf_cases)} CDF cases). "
+          f"These take about 30s each.")
+    run_cases(cdf_pdf_cases, run_cdf, "cdf_data")
+
+    print(f"Running 3rd batch ({len(moment_cases)} moment cases). "
+          f"These take about anywhere from a few hours to days each.")
+    run_cases(moment_cases, run_moment, "moment_data")
+
+    print(f"Test data generated in {time.perf_counter() - t_start}s")
+
+
+if __name__ == "__main__":
+    main()

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_axis_nan_policy.py

@@ -0,0 +1,541 @@
+# Many scipy.stats functions support `axis` and `nan_policy` parameters.
+# When the two are combined, it can be tricky to get all the behavior just
+# right. This file contains a suite of common tests for scipy.stats functions
+# that support `axis` and `nan_policy` and additional tests for some associated
+# functions in stats._util.
+
+from itertools import product, combinations_with_replacement
+import re
+import pickle
+import pytest
+
+import numpy as np
+from numpy.lib import NumpyVersion
+from numpy.testing import assert_allclose, assert_equal
+from scipy import stats
+
+
+axis_nan_policy_cases = [
+    # function, args, kwds, number of samples, paired, unpacker function
+    # args, kwds typically aren't needed; just showing that they work
+    (stats.kruskal, tuple(), dict(), 3, False, None),  # 4 samples is slow
+    (stats.ranksums, ('less',), dict(), 2, False, None),
+    (stats.mannwhitneyu, tuple(), {'method': 'asymptotic'}, 2, False, None),
+    (stats.wilcoxon, ('pratt',), {'mode': 'auto'}, 2, True, None),
+    (stats.wilcoxon, tuple(), dict(), 1, True, None),
+    ]
+
+# If the message is one of those expected, put nans in
+# appropriate places of `statistics` and `pvalues`
+too_small_messages = {"The input contains nan",  # for nan_policy="raise"
+                      "Degrees of freedom <= 0 for slice",
+                      "x and y should have at least 5 elements",
+                      "Data must be at least length 3",
+                      "The sample must contain at least two",
+                      "x and y must contain at least two",
+                      "division by zero",
+                      "Mean of empty slice",
+                      "Data passed to ks_2samp must not be empty",
+                      "Not enough test observations",
+                      "Not enough other observations",
+                      "At least one observation is required",
+                      "zero-size array to reduction operation maximum",
+                      "`x` and `y` must be of nonzero size.",
+                      "The exact distribution of the Wilcoxon test"}
+
+
+def _mixed_data_generator(n_samples, n_repetitions, axis, rng,
+                          paired=False):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and various
+    # nan patterns (e.g. all nans, some nans, no nans) along axis-slices
+
+    data = []
+    for i in range(n_samples):
+        n_patterns = 6  # number of distinct nan patterns
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        x = np.ones((n_repetitions, n_patterns, n_obs)) * np.nan
+
+        for j in range(n_repetitions):
+            samples = x[j, :, :]
+
+            # case 0: axis-slice with all nans (0 reals)
+            # cases 1-3: axis-slice with 1-3 reals (the rest nans)
+            # case 4: axis-slice with mostly (all but two) reals
+            # case 5: axis slice with all reals
+            for k, n_reals in enumerate([0, 1, 2, 3, n_obs-2, n_obs]):
+                # for cases 1-3, need paired nansw  to be in the same place
+                indices = rng.permutation(n_obs)[:n_reals]
+                samples[k, indices] = rng.random(size=n_reals)
+
+            # permute the axis-slices just to show that order doesn't matter
+            samples[:] = rng.permutation(samples, axis=0)
+
+        # For multi-sample tests, we want to test broadcasting and check
+        # that nan policy works correctly for each nan pattern for each input.
+        # This takes care of both simultaneosly.
+        new_shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        new_shape[1 + i] = 6
+        x = x.reshape(new_shape)
+
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def _homogeneous_data_generator(n_samples, n_repetitions, axis, rng,
+                                paired=False, all_nans=True):
+    # generate random samples to check the response of hypothesis tests to
+    # samples with different (but broadcastable) shapes and homogeneous
+    # data (all nans or all finite)
+    data = []
+    for i in range(n_samples):
+        n_obs = 20 if paired else 20 + i  # observations per axis-slice
+        shape = [n_repetitions] + [1]*n_samples + [n_obs]
+        shape[1 + i] = 2
+        x = np.ones(shape) * np.nan if all_nans else rng.random(shape)
+        x = np.moveaxis(x, -1, axis)
+        data.append(x)
+    return data
+
+
+def nan_policy_1d(hypotest, data1d, unpacker, *args,
+                  nan_policy='raise', paired=False, _no_deco=True, **kwds):
+    # Reference implementation for how `nan_policy` should work for 1d samples
+
+    if nan_policy == 'raise':
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                raise ValueError("The input contains nan values")
+
+    elif nan_policy == 'propagate':
+        # For all hypothesis tests tested, returning nans is the right thing.
+        # But many hypothesis tests don't propagate correctly (e.g. they treat
+        # np.nan the same as np.inf, which doesn't make sense when ranks are
+        # involved) so override that behavior here.
+        for sample in data1d:
+            if np.any(np.isnan(sample)):
+                return np.nan, np.nan
+
+    elif nan_policy == 'omit':
+        # manually omit nans (or pairs in which at least one element is nan)
+        if not paired:
+            data1d = [sample[~np.isnan(sample)] for sample in data1d]
+        else:
+            nan_mask = np.isnan(data1d[0])
+            for sample in data1d[1:]:
+                nan_mask = np.logical_or(nan_mask, np.isnan(sample))
+            data1d = [sample[~nan_mask] for sample in data1d]
+
+    return unpacker(hypotest(*data1d, *args, _no_deco=_no_deco, **kwds))
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "paired",
+                          "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("axis"), (1,))
+@pytest.mark.parametrize(("data_generator"), ("mixed",))
+def test_axis_nan_policy_fast(hypotest, args, kwds, n_samples, paired,
+                              unpacker, nan_policy, axis,
+                              data_generator):
+    _axis_nan_policy_test(hypotest, args, kwds, n_samples, paired,
+                          unpacker, nan_policy, axis, data_generator)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "paired",
+                          "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("axis"), range(-3, 3))
+@pytest.mark.parametrize(("data_generator"),
+                         ("all_nans", "all_finite", "mixed"))
+def test_axis_nan_policy_full(hypotest, args, kwds, n_samples, paired,
+                              unpacker, nan_policy, axis,
+                              data_generator):
+    _axis_nan_policy_test(hypotest, args, kwds, n_samples, paired,
+                          unpacker, nan_policy, axis, data_generator)
+
+
+def _axis_nan_policy_test(hypotest, args, kwds, n_samples, paired,
+                          unpacker, nan_policy, axis, data_generator):
+    # Tests the 1D and vectorized behavior of hypothesis tests against a
+    # reference implementation (nan_policy_1d with np.ndenumerate)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    if NumpyVersion(np.__version__) < '1.18.0':
+        pytest.xfail("Generator `permutation` method doesn't support `axis`")
+    rng = np.random.default_rng(0)
+
+    # Generate multi-dimensional test data with all important combinations
+    # of patterns of nans along `axis`
+    n_repetitions = 3  # number of repetitions of each pattern
+    data_gen_kwds = {'n_samples': n_samples, 'n_repetitions': n_repetitions,
+                     'axis': axis, 'rng': rng, 'paired': paired}
+    if data_generator == 'mixed':
+        inherent_size = 6  # number of distinct types of patterns
+        data = _mixed_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_nans':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = True
+        data = _homogeneous_data_generator(**data_gen_kwds)
+    elif data_generator == 'all_finite':
+        inherent_size = 2  # hard-coded in _homogeneous_data_generator
+        data_gen_kwds['all_nans'] = False
+        data = _homogeneous_data_generator(**data_gen_kwds)
+
+    output_shape = [n_repetitions] + [inherent_size]*n_samples
+
+    # To generate reference behavior to compare against, loop over the axis-
+    # slices in data. Make indexing easier by moving `axis` to the end and
+    # broadcasting all samples to the same shape.
+    data_b = [np.moveaxis(sample, axis, -1) for sample in data]
+    data_b = [np.broadcast_to(sample, output_shape + [sample.shape[-1]])
+              for sample in data_b]
+    statistics = np.zeros(output_shape)
+    pvalues = np.zeros(output_shape)
+
+    for i, _ in np.ndenumerate(statistics):
+        data1d = [sample[i] for sample in data_b]
+        with np.errstate(divide='ignore', invalid='ignore'):
+            try:
+                res1d = nan_policy_1d(hypotest, data1d, unpacker, *args,
+                                      nan_policy=nan_policy, paired=paired,
+                                      _no_deco=True, **kwds)
+
+                # Eventually we'll check the results of a single, vectorized
+                # call of `hypotest` against the arrays `statistics` and
+                # `pvalues` populated using the reference `nan_policy_1d`.
+                # But while we're at it, check the results of a 1D call to
+                # `hypotest` against the reference `nan_policy_1d`.
+                res1db = unpacker(hypotest(*data1d, *args,
+                                           nan_policy=nan_policy, **kwds))
+                assert_equal(res1db[0], res1d[0])
+                if len(res1db) == 2:
+                    assert_equal(res1db[1], res1d[1])
+
+            # When there is not enough data in 1D samples, many existing
+            # hypothesis tests raise errors instead of returning nans .
+            # For vectorized calls, we put nans in the corresponding elements
+            # of the output.
+            except (RuntimeWarning, ValueError, ZeroDivisionError) as e:
+
+                # whatever it is, make sure same error is raised by both
+                # `nan_policy_1d` and `hypotest`
+                with pytest.raises(type(e), match=re.escape(str(e))):
+                    nan_policy_1d(hypotest, data1d, unpacker, *args,
+                                  nan_policy=nan_policy, paired=paired,
+                                  _no_deco=True, **kwds)
+                with pytest.raises(type(e), match=re.escape(str(e))):
+                    hypotest(*data1d, *args, nan_policy=nan_policy, **kwds)
+
+                if any([str(e).startswith(message)
+                        for message in too_small_messages]):
+                    res1d = np.nan, np.nan
+                else:
+                    raise e
+        statistics[i] = res1d[0]
+        if len(res1d) == 2:
+            pvalues[i] = res1d[1]
+
+    # Perform a vectorized call to the hypothesis test.
+    # If `nan_policy == 'raise'`, check that it raises the appropriate error.
+    # If not, compare against the output against `statistics` and `pvalues`
+    if nan_policy == 'raise' and not data_generator == "all_finite":
+        message = 'The input contains nan values'
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=axis, nan_policy=nan_policy, *args, **kwds)
+
+    else:
+        with np.errstate(divide='ignore', invalid='ignore'):
+            res = unpacker(hypotest(*data, axis=axis, nan_policy=nan_policy,
+                                    *args, **kwds))
+
+        assert_equal(res[0], statistics)
+        assert_equal(res[0].dtype, statistics.dtype)
+        if len(res) == 2:
+            assert_equal(res[1], pvalues)
+            assert_equal(res[1].dtype, pvalues.dtype)
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "paired",
+                          "unpacker"), axis_nan_policy_cases)
+@pytest.mark.parametrize(("nan_policy"), ("propagate", "omit", "raise"))
+@pytest.mark.parametrize(("data_generator"),
+                         ("all_nans", "all_finite", "mixed", "empty"))
+def test_axis_nan_policy_axis_is_None(hypotest, args, kwds, n_samples, paired,
+                                      unpacker, nan_policy, data_generator):
+    # check for correct behavior when `axis=None`
+
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    if NumpyVersion(np.__version__) < '1.18.0':
+        pytest.xfail("Generator `permutation` method doesn't support `axis`")
+    rng = np.random.default_rng(0)
+
+    if data_generator == "empty":
+        data = [rng.random((2, 0)) for i in range(n_samples)]
+    else:
+        data = [rng.random((2, 20)) for i in range(n_samples)]
+
+    if data_generator == "mixed":
+        masks = [rng.random((2, 20)) > 0.9 for i in range(n_samples)]
+        for sample, mask in zip(data, masks):
+            sample[mask] = np.nan
+    elif data_generator == "all_nans":
+        data = [sample * np.nan for sample in data]
+
+    data_raveled = [sample.ravel() for sample in data]
+
+    if nan_policy == 'raise' and data_generator not in {"all_finite", "empty"}:
+        message = 'The input contains nan values'
+
+        # check for correct behavior whether or not data is 1d to begin with
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+        with pytest.raises(ValueError, match=message):
+            hypotest(*data_raveled, axis=None, nan_policy=nan_policy,
+                     *args, **kwds)
+
+    else:
+        # behavior of reference implementation with 1d input, hypotest with 1d
+        # input, and hypotest with Nd input should match, whether that means
+        # that outputs are equal or they raise the same exception
+
+        ea_str, eb_str, ec_str = None, None, None
+        with np.errstate(divide='ignore', invalid='ignore'):
+            try:
+                res1da = nan_policy_1d(hypotest, data_raveled, unpacker, *args,
+                                       nan_policy=nan_policy, paired=paired,
+                                       _no_deco=True, **kwds)
+            except (RuntimeWarning, ValueError, ZeroDivisionError) as ea:
+                ea_str = str(ea)
+
+            try:
+                res1db = unpacker(hypotest(*data_raveled, *args,
+                                           nan_policy=nan_policy, **kwds))
+            except (RuntimeWarning, ValueError, ZeroDivisionError) as eb:
+                eb_str = str(eb)
+
+            try:
+                res1dc = unpacker(hypotest(*data, *args, axis=None,
+                                           nan_policy=nan_policy, **kwds))
+            except (RuntimeWarning, ValueError, ZeroDivisionError) as ec:
+                ec_str = str(ec)
+
+            if ea_str or eb_str or ec_str:
+                assert any([str(ea_str).startswith(message)
+                            for message in too_small_messages])
+                assert ea_str == eb_str == ec_str
+            else:
+                assert_equal(res1db, res1da)
+                assert_equal(res1dc, res1da)
+
+
+@pytest.mark.parametrize(("axis"), (0, 1, 2))
+def test_axis_nan_policy_decorated_positional_axis(axis):
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether `axis` is provided as positional or
+    # keyword argument
+    if NumpyVersion(np.__version__) < '1.18.0':
+        pytest.xfail("Avoid test failures due to old version of NumPy")
+
+    shape = (8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    y = rng.random(shape)
+    res1 = stats.mannwhitneyu(x, y, True, 'two-sided', axis)
+    res2 = stats.mannwhitneyu(x, y, True, 'two-sided', axis=axis)
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument 'axis'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(x, y, True, 'two-sided', axis, axis=axis)
+
+
+def test_axis_nan_policy_decorated_positional_args():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator when function accepts *args
+    if NumpyVersion(np.__version__) < '1.18.0':
+        pytest.xfail("Avoid test failures due to old version of NumPy")
+
+    shape = (3, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    stats.kruskal(*x)
+
+    message = "kruskal() got an unexpected keyword argument 'args'"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(args=x)
+
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.kruskal(*x, args=x)
+
+
+def test_axis_nan_policy_decorated_keyword_samples():
+    # Test for correct behavior of function decorated with
+    # _axis_nan_policy_decorator whether samples are provided as positional or
+    # keyword arguments
+    if NumpyVersion(np.__version__) < '1.18.0':
+        pytest.xfail("Avoid test failures due to old version of NumPy")
+
+    shape = (2, 8, 9, 10)
+    rng = np.random.default_rng(0)
+    x = rng.random(shape)
+    x[0, 0, 0, 0] = np.nan
+    res1 = stats.mannwhitneyu(*x)
+    res2 = stats.mannwhitneyu(x=x[0], y=x[1])
+    assert_equal(res1, res2)
+
+    message = "mannwhitneyu() got multiple values for argument"
+    with pytest.raises(TypeError, match=re.escape(message)):
+        stats.mannwhitneyu(*x, x=x[0], y=x[1])
+
+
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "paired",
+                          "unpacker"), axis_nan_policy_cases)
+def test_axis_nan_policy_decorated_pickled(hypotest, args, kwds, n_samples,
+                                           paired, unpacker):
+    if NumpyVersion(np.__version__) < '1.18.0':
+        rng = np.random.RandomState(0)
+    else:
+        rng = np.random.default_rng(0)
+
+    # Some hypothesis tests return a non-iterable that needs an `unpacker` to
+    # extract the statistic and p-value. For those that don't:
+    if not unpacker:
+        def unpacker(res):
+            return res
+
+    data = rng.uniform(size=(n_samples, 2, 30))
+    pickled_hypotest = pickle.dumps(hypotest)
+    unpickled_hypotest = pickle.loads(pickled_hypotest)
+    res1 = unpacker(hypotest(*data, *args, axis=-1, **kwds))
+    res2 = unpacker(unpickled_hypotest(*data, *args, axis=-1, **kwds))
+    assert_allclose(res1, res2, rtol=1e-12)
+
+
+def test_check_empty_inputs():
+    # Test that _check_empty_inputs is doing its job, at least for single-
+    # sample inputs. (Multi-sample functionality is tested below.)
+    # If the input sample is not empty, it should return None.
+    # If the input sample is empty, it should return an array of NaNs or an
+    # empty array of appropriate shape. np.mean is used as a reference for the
+    # output because, like the statistics calculated by these functions,
+    # it works along and "consumes" `axis` but preserves the other axes.
+    for i in range(5):
+        for combo in combinations_with_replacement([0, 1, 2], i):
+            for axis in range(len(combo)):
+                samples = (np.zeros(combo),)
+                output = stats._axis_nan_policy._check_empty_inputs(samples,
+                                                                    axis)
+                if output is not None:
+                    with np.testing.suppress_warnings() as sup:
+                        sup.filter(RuntimeWarning, "Mean of empty slice.")
+                        sup.filter(RuntimeWarning, "invalid value encountered")
+                        reference = samples[0].mean(axis=axis)
+                    np.testing.assert_equal(output, reference)
+
+
+def _check_arrays_broadcastable(arrays, axis):
+    # https://numpy.org/doc/stable/user/basics.broadcasting.html
+    # "When operating on two arrays, NumPy compares their shapes element-wise.
+    # It starts with the trailing (i.e. rightmost) dimensions and works its
+    # way left.
+    # Two dimensions are compatible when
+    # 1. they are equal, or
+    # 2. one of them is 1
+    # ...
+    # Arrays do not need to have the same number of dimensions."
+    # (Clarification: if the arrays are compatible according to the criteria
+    #  above and an array runs out of dimensions, it is still compatible.)
+    # Below, we follow the rules above except ignoring `axis`
+
+    n_dims = max([arr.ndim for arr in arrays])
+    if axis is not None:
+        # convert to negative axis
+        axis = (-n_dims + axis) if axis >= 0 else axis
+
+    for dim in range(1, n_dims+1):  # we'll index from -1 to -n_dims, inclusive
+        if -dim == axis:
+            continue  # ignore lengths along `axis`
+
+        dim_lengths = set()
+        for arr in arrays:
+            if dim <= arr.ndim and arr.shape[-dim] != 1:
+                dim_lengths.add(arr.shape[-dim])
+
+        if len(dim_lengths) > 1:
+            return False
+    return True
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize(("hypotest", "args", "kwds", "n_samples", "paired",
+                          "unpacker"), axis_nan_policy_cases)
+def test_empty(hypotest, args, kwds, n_samples, paired, unpacker):
+    # test for correct output shape when at least one input is empty
+
+    def small_data_generator(n_samples, n_dims):
+
+        def small_sample_generator(n_dims):
+            # return all possible "small" arrays in up to n_dim dimensions
+            for i in n_dims:
+                # "small" means with size along dimension either 0 or 1
+                for combo in combinations_with_replacement([0, 1, 2], i):
+                    yield np.zeros(combo)
+
+        # yield all possible combinations of small samples
+        gens = [small_sample_generator(n_dims) for i in range(n_samples)]
+        for i in product(*gens):
+            yield i
+
+    n_dims = [2, 3]
+    for samples in small_data_generator(n_samples, n_dims):
+
+        # this test is only for arrays of zero size
+        if not any((sample.size == 0 for sample in samples)):
+            continue
+
+        max_axis = max((sample.ndim for sample in samples))
+
+        # need to test for all valid values of `axis` parameter, too
+        for axis in range(-max_axis, max_axis):
+
+            try:
+                # After broadcasting, all arrays are the same shape, so
+                # the shape of the output should be the same as a single-
+                # sample statistic. Use np.mean as a reference.
+                concat = stats._stats_py._broadcast_concatenate(samples, axis)
+                with np.testing.suppress_warnings() as sup:
+                    sup.filter(RuntimeWarning, "Mean of empty slice.")
+                    sup.filter(RuntimeWarning, "invalid value encountered")
+                    expected = np.mean(concat, axis=axis) * np.nan
+
+                res = hypotest(*samples, *args, axis=axis, **kwds)
+
+                if hasattr(res, 'statistic'):
+                    assert_equal(res.statistic, expected)
+                    assert_equal(res.pvalue, expected)
+                else:
+                    assert_equal(res, expected)
+
+            except ValueError:
+                # confirm that the arrays truly are not broadcastable
+                assert not _check_arrays_broadcastable(samples, axis)
+
+                # confirm that _both_ `_broadcast_concatenate` and `hypotest`
+                # produce this information.
+                message = "Array shapes are incompatible for broadcasting."
+                with pytest.raises(ValueError, match=message):
+                    stats._stats_py._broadcast_concatenate(samples, axis)
+                with pytest.raises(ValueError, match=message):
+                    hypotest(*samples, *args, axis=axis, **kwds)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_binned_statistic.py

@@ -0,0 +1,542 @@
+import numpy as np
+from numpy.testing import assert_allclose
+from pytest import raises as assert_raises
+from scipy.stats import (binned_statistic, binned_statistic_2d,
+                         binned_statistic_dd)
+from scipy._lib._util import check_random_state
+
+from .common_tests import check_named_results
+
+
+class TestBinnedStatistic:
+
+    @classmethod
+    def setup_class(cls):
+        rng = check_random_state(9865)
+        cls.x = rng.uniform(size=100)
+        cls.y = rng.uniform(size=100)
+        cls.v = rng.uniform(size=100)
+        cls.X = rng.uniform(size=(100, 3))
+        cls.w = rng.uniform(size=100)
+        cls.u = rng.uniform(size=100) + 1e6
+
+    def test_1d_count(self):
+        x = self.x
+        v = self.v
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=10)
+        count2, edges2 = np.histogram(x, bins=10)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_gh5927(self):
+        # smoke test for gh5927 - binned_statistic was using `is` for string
+        # comparison
+        x = self.x
+        v = self.v
+        statistics = [u'mean', u'median', u'count', u'sum']
+        for statistic in statistics:
+            binned_statistic(x, v, statistic, bins=10)
+
+    def test_big_number_std(self):
+        # tests for numerical stability of std calculation
+        # see issue gh-10126 for more
+        x = self.x
+        u = self.u
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+
+    def test_empty_bins_std(self):
+        # tests that std returns gives nan for empty bins
+        x = self.x
+        u = self.u
+        print(binned_statistic(x, u, 'count', bins=1000))
+        stat1, edges1, bc = binned_statistic(x, u, 'std', bins=1000)
+        stat2, edges2, bc = binned_statistic(x, u, np.std, bins=1000)
+
+        assert_allclose(stat1, stat2)
+
+    def test_non_finite_inputs_and_int_bins(self):
+        # if either `values` or `sample` contain np.inf or np.nan throw
+        # see issue gh-9010 for more
+        x = self.x
+        u = self.u
+        orig = u[0]
+        u[0] = np.inf
+        assert_raises(ValueError, binned_statistic, u, x, 'std', bins=10)
+        # need to test for non-python specific ints, e.g. np.int8, np.int64
+        assert_raises(ValueError, binned_statistic, u, x, 'std',
+                      bins=np.int64(10))
+        u[0] = np.nan
+        assert_raises(ValueError, binned_statistic, u, x, 'count', bins=10)
+        # replace original value, u belongs the class
+        u[0] = orig
+
+    def test_1d_result_attributes(self):
+        x = self.x
+        v = self.v
+
+        res = binned_statistic(x, v, 'count', bins=10)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_1d_sum(self):
+        x = self.x
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic(x, v, 'sum', bins=10)
+        sum2, edges2 = np.histogram(x, bins=10, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_mean(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'mean', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.mean, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_std(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.std, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_min(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'min', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.min, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_max(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'max', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.max, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_median(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'median', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.median, bins=10)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_1d_bincode(self):
+        x = self.x[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=3)
+        bc2 = np.array([3, 2, 1, 3, 2, 3, 3, 3, 3, 1, 1, 3, 3, 1, 2, 3, 1,
+                        1, 2, 1])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        assert_allclose(bcount, count1)
+
+    def test_1d_range_keyword(self):
+        # Regression test for gh-3063, range can be (min, max) or [(min, max)]
+        np.random.seed(9865)
+        x = np.arange(30)
+        data = np.random.random(30)
+
+        mean, bins, _ = binned_statistic(x[:15], data[:15])
+        mean_range, bins_range, _ = binned_statistic(x, data, range=[(0, 14)])
+        mean_range2, bins_range2, _ = binned_statistic(x, data, range=(0, 14))
+
+        assert_allclose(mean, mean_range)
+        assert_allclose(bins, bins_range)
+        assert_allclose(mean, mean_range2)
+        assert_allclose(bins, bins_range2)
+
+    def test_1d_multi_values(self):
+        x = self.x
+        v = self.v
+        w = self.w
+
+        stat1v, edges1v, bc1v = binned_statistic(x, v, 'mean', bins=10)
+        stat1w, edges1w, bc1w = binned_statistic(x, w, 'mean', bins=10)
+        stat2, edges2, bc2 = binned_statistic(x, [v, w], 'mean', bins=10)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(edges1v, edges2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_count(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=5)
+        count2, binx2, biny2 = np.histogram2d(x, y, bins=5)
+
+        assert_allclose(count1, count2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_result_attributes(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        res = binned_statistic_2d(x, y, v, 'count', bins=5)
+        attributes = ('statistic', 'x_edge', 'y_edge', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_2d_sum(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        sum1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'sum', bins=5)
+        sum2, binx2, biny2 = np.histogram2d(x, y, bins=5, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_mean_unicode(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_std(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'std', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.std, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_min(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'min', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.min, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_max(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'max', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.max, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_median(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'median', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(
+            x, y, v, np.median, bins=5)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(binx1, binx2)
+        assert_allclose(biny1, biny2)
+
+    def test_2d_bincode(self):
+        x = self.x[:20]
+        y = self.y[:20]
+        v = self.v[:20]
+
+        count1, binx1, biny1, bc = binned_statistic_2d(
+            x, y, v, 'count', bins=3)
+        bc2 = np.array([17, 11, 6, 16, 11, 17, 18, 17, 17, 7, 6, 18, 16,
+                        6, 11, 16, 6, 6, 11, 8])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_2d_multi_values(self):
+        x = self.x
+        y = self.y
+        v = self.v
+        w = self.w
+
+        stat1v, binx1v, biny1v, bc1v = binned_statistic_2d(
+            x, y, v, 'mean', bins=8)
+        stat1w, binx1w, biny1w, bc1w = binned_statistic_2d(
+            x, y, w, 'mean', bins=8)
+        stat2, binx2, biny2, bc2 = binned_statistic_2d(
+            x, y, [v, w], 'mean', bins=8)
+
+        assert_allclose(stat2[0], stat1v)
+        assert_allclose(stat2[1], stat1w)
+        assert_allclose(binx1v, binx2)
+        assert_allclose(biny1w, biny2)
+        assert_allclose(bc1v, bc2)
+
+    def test_2d_binnumbers_unraveled(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(x, v, 'mean', bins=20)
+        stat, edgesy, bcy = binned_statistic(y, v, 'mean', bins=10)
+
+        stat2, edgesx2, edgesy2, bc2 = binned_statistic_2d(
+            x, y, v, 'mean', bins=(20, 10), expand_binnumbers=True)
+
+        bcx3 = np.searchsorted(edgesx, x, side='right')
+        bcy3 = np.searchsorted(edgesy, y, side='right')
+
+        # `numpy.searchsorted` is non-inclusive on right-edge, compensate
+        bcx3[x == x.max()] -= 1
+        bcy3[y == y.max()] -= 1
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcx3, bc2[0])
+        assert_allclose(bcy3, bc2[1])
+
+    def test_dd_count(self):
+        X = self.X
+        v = self.v
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        count2, edges2 = np.histogramdd(X, bins=3)
+
+        assert_allclose(count1, count2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_result_attributes(self):
+        X = self.X
+        v = self.v
+
+        res = binned_statistic_dd(X, v, 'count', bins=3)
+        attributes = ('statistic', 'bin_edges', 'binnumber')
+        check_named_results(res, attributes)
+
+    def test_dd_sum(self):
+        X = self.X
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic_dd(X, v, 'sum', bins=3)
+        sum2, edges2 = np.histogramdd(X, bins=3, weights=v)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_mean(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'mean', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.mean, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_std(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'std', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.std, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_min(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'min', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.min, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_max(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'max', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.max, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_median(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'median', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.median, bins=3)
+
+        assert_allclose(stat1, stat2)
+        assert_allclose(edges1, edges2)
+
+    def test_dd_bincode(self):
+        X = self.X[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        bc2 = np.array([63, 33, 86, 83, 88, 67, 57, 33, 42, 41, 82, 83, 92,
+                        32, 36, 91, 43, 87, 81, 81])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_allclose(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_allclose(bcount, count1adj)
+
+    def test_dd_multi_values(self):
+        X = self.X
+        v = self.v
+        w = self.w
+
+        for stat in ["count", "sum", "mean", "std", "min", "max", "median",
+                     np.std]:
+            stat1v, edges1v, bc1v = binned_statistic_dd(X, v, stat, bins=8)
+            stat1w, edges1w, bc1w = binned_statistic_dd(X, w, stat, bins=8)
+            stat2, edges2, bc2 = binned_statistic_dd(X, [v, w], stat, bins=8)
+            assert_allclose(stat2[0], stat1v)
+            assert_allclose(stat2[1], stat1w)
+            assert_allclose(edges1v, edges2)
+            assert_allclose(edges1w, edges2)
+            assert_allclose(bc1v, bc2)
+
+    def test_dd_binnumbers_unraveled(self):
+        X = self.X
+        v = self.v
+
+        stat, edgesx, bcx = binned_statistic(X[:, 0], v, 'mean', bins=15)
+        stat, edgesy, bcy = binned_statistic(X[:, 1], v, 'mean', bins=20)
+        stat, edgesz, bcz = binned_statistic(X[:, 2], v, 'mean', bins=10)
+
+        stat2, edges2, bc2 = binned_statistic_dd(
+            X, v, 'mean', bins=(15, 20, 10), expand_binnumbers=True)
+
+        assert_allclose(bcx, bc2[0])
+        assert_allclose(bcy, bc2[1])
+        assert_allclose(bcz, bc2[2])
+
+    def test_dd_binned_statistic_result(self):
+        # NOTE: tests the reuse of bin_edges from previous call
+        x = np.random.random((10000, 3))
+        v = np.random.random((10000))
+        bins = np.linspace(0, 1, 10)
+        bins = (bins, bins, bins)
+
+        result = binned_statistic_dd(x, v, 'mean', bins=bins)
+        stat = result.statistic
+
+        result = binned_statistic_dd(x, v, 'mean',
+                                     binned_statistic_result=result)
+        stat2 = result.statistic
+
+        assert_allclose(stat, stat2)
+
+    def test_dd_zero_dedges(self):
+        x = np.random.random((10000, 3))
+        v = np.random.random((10000))
+        bins = np.linspace(0, 1, 10)
+        bins = np.append(bins, 1)
+        bins = (bins, bins, bins)
+        with assert_raises(ValueError, match='difference is numerically 0'):
+            binned_statistic_dd(x, v, 'mean', bins=bins)
+
+    def test_dd_range_errors(self):
+        # Test that descriptive exceptions are raised as appropriate for bad
+        # values of the `range` argument. (See gh-12996)
+        with assert_raises(ValueError,
+                           match='In range, start must be <= stop'):
+            binned_statistic_dd([self.y], self.v,
+                                range=[[1, 0]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 1 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[1, 0], [0, 1]])
+        with assert_raises(
+                ValueError,
+                match='In dimension 2 of range, start must be <= stop'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1], [1, 0]])
+        with assert_raises(
+                ValueError,
+                match='range given for 1 dimensions; 2 required'):
+            binned_statistic_dd([self.x, self.y], self.v,
+                                range=[[0, 1]])
+
+    def test_binned_statistic_float32(self):
+        X = np.array([0, 0.42358226], dtype=np.float32)
+        stat, _, _ = binned_statistic(X, None, 'count', bins=5)
+        assert_allclose(stat, np.array([1, 0, 0, 0, 1], dtype=np.float64))
+
+    def test_gh14332(self):
+        # Test the wrong output when the `sample` is close to bin edge
+        x = []
+        size = 20
+        for i in range(size):
+            x += [1-0.1**i]
+ 
+        bins = np.linspace(0,1,11)
+        sum1, edges1, bc = binned_statistic_dd(x, np.ones(len(x)),
+                                               bins=[bins], statistic='sum')
+        sum2, edges2 = np.histogram(x, bins=bins)
+
+        assert_allclose(sum1, sum2)
+        assert_allclose(edges1[0], edges2)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_bootstrap.py

@@ -0,0 +1,490 @@
+import numpy as np
+import pytest
+from scipy.stats import bootstrap, BootstrapDegenerateDistributionWarning
+from numpy.testing import assert_allclose, assert_equal
+from scipy import stats
+from .. import _bootstrap as _bootstrap
+from scipy._lib._util import rng_integers
+
+
+def test_bootstrap_iv():
+
+    message = "`data` must be a sequence of samples."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(1, np.mean)
+
+    message = "`data` must contain at least one sample."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(tuple(), np.mean)
+
+    message = "each sample in `data` must contain two or more observations..."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3], [1]), np.mean)
+
+    message = ("When `paired is True`, all samples must have the same length ")
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3], [1, 2, 3, 4]), np.mean, paired=True)
+
+    message = "`vectorized` must be `True` or `False`."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(1, np.mean, vectorized='ekki')
+
+    message = "`axis` must be an integer."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, axis=1.5)
+
+    message = "could not convert string to float"
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, confidence_level='ni')
+
+    message = "`n_resamples` must be a positive integer."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, n_resamples=-1000)
+
+    message = "`n_resamples` must be a positive integer."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, n_resamples=1000.5)
+
+    message = "`batch` must be a positive integer or None."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, batch=-1000)
+
+    message = "`batch` must be a positive integer or None."
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, batch=1000.5)
+
+    message = "`method` must be in"
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, method='ekki')
+
+    message = "`method = 'BCa' is only available for one-sample statistics"
+
+    def statistic(x, y, axis):
+        mean1 = np.mean(x, axis)
+        mean2 = np.mean(y, axis)
+        return mean1 - mean2
+
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([.1, .2, .3], [.1, .2, .3]), statistic, method='BCa')
+
+    message = "'herring' cannot be used to seed a"
+    with pytest.raises(ValueError, match=message):
+        bootstrap(([1, 2, 3],), np.mean, random_state='herring')
+
+
+@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+@pytest.mark.parametrize("axis", [0, 1, 2])
+def test_bootstrap_batch(method, axis):
+    # for one-sample statistics, batch size shouldn't affect the result
+    np.random.seed(0)
+
+    x = np.random.rand(10, 11, 12)
+    res1 = bootstrap((x,), np.mean, batch=None, method=method,
+                     random_state=0, axis=axis, n_resamples=100)
+    res2 = bootstrap((x,), np.mean, batch=10, method=method,
+                     random_state=0, axis=axis, n_resamples=100)
+
+    assert_equal(res2.confidence_interval.low, res1.confidence_interval.low)
+    assert_equal(res2.confidence_interval.high, res1.confidence_interval.high)
+    assert_equal(res2.standard_error, res1.standard_error)
+
+
+@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+def test_bootstrap_paired(method):
+    # test that `paired` works as expected
+    np.random.seed(0)
+    n = 100
+    x = np.random.rand(n)
+    y = np.random.rand(n)
+
+    def my_statistic(x, y, axis=-1):
+        return ((x-y)**2).mean(axis=axis)
+
+    def my_paired_statistic(i, axis=-1):
+        a = x[i]
+        b = y[i]
+        res = my_statistic(a, b)
+        return res
+
+    i = np.arange(len(x))
+
+    res1 = bootstrap((i,), my_paired_statistic, random_state=0)
+    res2 = bootstrap((x, y), my_statistic, paired=True, random_state=0)
+
+    assert_allclose(res1.confidence_interval, res2.confidence_interval)
+    assert_allclose(res1.standard_error, res2.standard_error)
+
+
+@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+@pytest.mark.parametrize("axis", [0, 1, 2])
+@pytest.mark.parametrize("paired", [True, False])
+def test_bootstrap_vectorized(method, axis, paired):
+    # test that paired is vectorized as expected: when samples are tiled,
+    # CI and standard_error of each axis-slice is the same as those of the
+    # original 1d sample
+
+    if not paired and method == 'BCa':
+        # should re-assess when BCa is extended
+        pytest.xfail(reason="BCa currently for 1-sample statistics only")
+    np.random.seed(0)
+
+    def my_statistic(x, y, z, axis=-1):
+        return x.mean(axis=axis) + y.mean(axis=axis) + z.mean(axis=axis)
+
+    shape = 10, 11, 12
+    n_samples = shape[axis]
+
+    x = np.random.rand(n_samples)
+    y = np.random.rand(n_samples)
+    z = np.random.rand(n_samples)
+    res1 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
+                     random_state=0, axis=0, n_resamples=100)
+
+    reshape = [1, 1, 1]
+    reshape[axis] = n_samples
+    x = np.broadcast_to(x.reshape(reshape), shape)
+    y = np.broadcast_to(y.reshape(reshape), shape)
+    z = np.broadcast_to(z.reshape(reshape), shape)
+    res2 = bootstrap((x, y, z), my_statistic, paired=paired, method=method,
+                     random_state=0, axis=axis, n_resamples=100)
+
+    assert_allclose(res2.confidence_interval.low,
+                    res1.confidence_interval.low)
+    assert_allclose(res2.confidence_interval.high,
+                    res1.confidence_interval.high)
+    assert_allclose(res2.standard_error, res1.standard_error)
+
+    result_shape = list(shape)
+    result_shape.pop(axis)
+
+    assert_equal(res2.confidence_interval.low.shape, result_shape)
+    assert_equal(res2.confidence_interval.high.shape, result_shape)
+    assert_equal(res2.standard_error.shape, result_shape)
+
+
+@pytest.mark.parametrize("method", ['basic', 'percentile', 'BCa'])
+def test_bootstrap_against_theory(method):
+    # based on https://www.statology.org/confidence-intervals-python/
+    data = stats.norm.rvs(loc=5, scale=2, size=5000, random_state=0)
+    alpha = 0.95
+    dist = stats.t(df=len(data)-1, loc=np.mean(data), scale=stats.sem(data))
+    expected_interval = dist.interval(alpha=alpha)
+    expected_se = dist.std()
+
+    res = bootstrap((data,), np.mean, n_resamples=5000,
+                    confidence_level=alpha, method=method,
+                    random_state=0)
+    assert_allclose(res.confidence_interval, expected_interval, rtol=5e-4)
+    assert_allclose(res.standard_error, expected_se, atol=3e-4)
+
+
+tests_R = {"basic": (23.77, 79.12),
+           "percentile": (28.86, 84.21),
+           "BCa": (32.31, 91.43)}
+
+
+@pytest.mark.parametrize("method, expected", tests_R.items())
+def test_bootstrap_against_R(method, expected):
+    # Compare against R's "boot" library
+    # library(boot)
+
+    # stat <- function (x, a) {
+    #     mean(x[a])
+    # }
+
+    # x <- c(10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
+    #        23, 34, 50, 81, 89, 121, 134, 213)
+
+    # # Use a large value so we get a few significant digits for the CI.
+    # n = 1000000
+    # bootresult = boot(x, stat, n)
+    # result <- boot.ci(bootresult)
+    # print(result)
+    x = np.array([10, 12, 12.5, 12.5, 13.9, 15, 21, 22,
+                  23, 34, 50, 81, 89, 121, 134, 213])
+    res = bootstrap((x,), np.mean, n_resamples=1000000, method=method,
+                    random_state=0)
+    assert_allclose(res.confidence_interval, expected, rtol=0.005)
+
+
+tests_against_itself_1samp = {"basic": 1780,
+                              "percentile": 1784,
+                              "BCa": 1784}
+
+
+@pytest.mark.parametrize("method, expected",
+                         tests_against_itself_1samp.items())
+def test_bootstrap_against_itself_1samp(method, expected):
+    # The expected values in this test were generated using bootstrap
+    # to check for unintended changes in behavior. The test also makes sure
+    # that bootstrap works with multi-sample statistics and that the
+    # `axis` argument works as expected / function is vectorized.
+    np.random.seed(0)
+
+    n = 100  # size of sample
+    n_resamples = 999  # number of bootstrap resamples used to form each CI
+    confidence_level = 0.9
+
+    # The true mean is 5
+    dist = stats.norm(loc=5, scale=1)
+    stat_true = dist.mean()
+
+    # Do the same thing 2000 times. (The code is fully vectorized.)
+    n_replications = 2000
+    data = dist.rvs(size=(n_replications, n))
+    res = bootstrap((data,),
+                    statistic=np.mean,
+                    confidence_level=confidence_level,
+                    n_resamples=n_resamples,
+                    batch=50,
+                    method=method,
+                    axis=-1)
+    ci = res.confidence_interval
+
+    # ci contains vectors of lower and upper confidence interval bounds
+    ci_contains_true = np.sum((ci[0] < stat_true) & (stat_true < ci[1]))
+    assert ci_contains_true == expected
+
+    # ci_contains_true is not inconsistent with confidence_level
+    pvalue = stats.binomtest(ci_contains_true, n_replications,
+                             confidence_level).pvalue
+    assert pvalue > 0.1
+
+
+tests_against_itself_2samp = {"basic": 892,
+                              "percentile": 890}
+
+
+@pytest.mark.parametrize("method, expected",
+                         tests_against_itself_2samp.items())
+def test_bootstrap_against_itself_2samp(method, expected):
+    # The expected values in this test were generated using bootstrap
+    # to check for unintended changes in behavior. The test also makes sure
+    # that bootstrap works with multi-sample statistics and that the
+    # `axis` argument works as expected / function is vectorized.
+    np.random.seed(0)
+
+    n1 = 100  # size of sample 1
+    n2 = 120  # size of sample 2
+    n_resamples = 999  # number of bootstrap resamples used to form each CI
+    confidence_level = 0.9
+
+    # The statistic we're interested in is the difference in means
+    def my_stat(data1, data2, axis=-1):
+        mean1 = np.mean(data1, axis=axis)
+        mean2 = np.mean(data2, axis=axis)
+        return mean1 - mean2
+
+    # The true difference in the means is -0.1
+    dist1 = stats.norm(loc=0, scale=1)
+    dist2 = stats.norm(loc=0.1, scale=1)
+    stat_true = dist1.mean() - dist2.mean()
+
+    # Do the same thing 1000 times. (The code is fully vectorized.)
+    n_replications = 1000
+    data1 = dist1.rvs(size=(n_replications, n1))
+    data2 = dist2.rvs(size=(n_replications, n2))
+    res = bootstrap((data1, data2),
+                    statistic=my_stat,
+                    confidence_level=confidence_level,
+                    n_resamples=n_resamples,
+                    batch=50,
+                    method=method,
+                    axis=-1)
+    ci = res.confidence_interval
+
+    # ci contains vectors of lower and upper confidence interval bounds
+    ci_contains_true = np.sum((ci[0] < stat_true) & (stat_true < ci[1]))
+    assert ci_contains_true == expected
+
+    # ci_contains_true is not inconsistent with confidence_level
+    pvalue = stats.binomtest(ci_contains_true, n_replications,
+                             confidence_level).pvalue
+    assert pvalue > 0.1
+
+
+@pytest.mark.parametrize("method", ["basic", "percentile"])
+@pytest.mark.parametrize("axis", [0, 1])
+def test_bootstrap_vectorized_3samp(method, axis):
+    def statistic(*data, axis=0):
+        # an arbitrary, vectorized statistic
+        return sum((sample.mean(axis) for sample in data))
+
+    def statistic_1d(*data):
+        # the same statistic, not vectorized
+        for sample in data:
+            assert sample.ndim == 1
+        return statistic(*data, axis=0)
+
+    np.random.seed(0)
+    x = np.random.rand(4, 5)
+    y = np.random.rand(4, 5)
+    z = np.random.rand(4, 5)
+    res1 = bootstrap((x, y, z), statistic, vectorized=True,
+                     axis=axis, n_resamples=100, method=method, random_state=0)
+    res2 = bootstrap((x, y, z), statistic_1d, vectorized=False,
+                     axis=axis, n_resamples=100, method=method, random_state=0)
+    assert_allclose(res1.confidence_interval, res2.confidence_interval)
+    assert_allclose(res1.standard_error, res2.standard_error)
+
+
+@pytest.mark.xfail_on_32bit("Failure is not concerning; see gh-14107")
+@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+@pytest.mark.parametrize("axis", [0, 1])
+def test_bootstrap_vectorized_1samp(method, axis):
+    def statistic(x, axis=0):
+        # an arbitrary, vectorized statistic
+        return x.mean(axis=axis)
+
+    def statistic_1d(x):
+        # the same statistic, not vectorized
+        assert x.ndim == 1
+        return statistic(x, axis=0)
+
+    np.random.seed(0)
+    x = np.random.rand(4, 5)
+    res1 = bootstrap((x,), statistic, vectorized=True, axis=axis,
+                     n_resamples=100, batch=None, method=method,
+                     random_state=0)
+    res2 = bootstrap((x,), statistic_1d, vectorized=False, axis=axis,
+                     n_resamples=100, batch=10, method=method,
+                     random_state=0)
+    assert_allclose(res1.confidence_interval, res2.confidence_interval)
+    assert_allclose(res1.standard_error, res2.standard_error)
+
+
+@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+def test_bootstrap_degenerate(method):
+    data = 35 * [10000.]
+    if method == "BCa":
+        with np.errstate(invalid='ignore'):
+            with pytest.warns(BootstrapDegenerateDistributionWarning):
+                res = bootstrap([data, ], np.mean, method=method)
+                assert_equal(res.confidence_interval, (np.nan, np.nan))
+    else:
+        res = bootstrap([data, ], np.mean, method=method)
+        assert_equal(res.confidence_interval, (10000., 10000.))
+    assert_equal(res.standard_error, 0)
+
+
+@pytest.mark.parametrize("method", ["basic", "percentile", "BCa"])
+def test_bootstrap_gh15678(method):
+    # Check that gh-15678 is fixed: when statistic function returned a Python
+    # float, method="BCa" failed when trying to add a dimension to the float
+    rng = np.random.default_rng(354645618886684)
+    dist = stats.norm(loc=2, scale=4)
+    data = dist.rvs(size=100, random_state=rng)
+    data = (data,)
+    res = bootstrap(data, stats.skew, method=method, n_resamples=100,
+                    random_state=np.random.default_rng(9563))
+    # this always worked because np.apply_along_axis returns NumPy data type
+    ref = bootstrap(data, stats.skew, method=method, n_resamples=100,
+                    random_state=np.random.default_rng(9563), vectorized=False)
+    assert_allclose(res.confidence_interval, ref.confidence_interval)
+    assert_allclose(res.standard_error, ref.standard_error)
+    assert isinstance(res.standard_error, np.float64)
+
+
+def test_jackknife_resample():
+    shape = 3, 4, 5, 6
+    np.random.seed(0)
+    x = np.random.rand(*shape)
+    y = next(_bootstrap._jackknife_resample(x))
+
+    for i in range(shape[-1]):
+        # each resample is indexed along second to last axis
+        # (last axis is the one the statistic will be taken over / consumed)
+        slc = y[..., i, :]
+        expected = np.delete(x, i, axis=-1)
+
+        assert np.array_equal(slc, expected)
+
+    y2 = np.concatenate(list(_bootstrap._jackknife_resample(x, batch=2)),
+                        axis=-2)
+    assert np.array_equal(y2, y)
+
+
+@pytest.mark.parametrize("rng_name", ["RandomState", "default_rng"])
+def test_bootstrap_resample(rng_name):
+    rng = getattr(np.random, rng_name, None)
+    if rng is None:
+        pytest.skip(f"{rng_name} not available.")
+    rng1 = rng(0)
+    rng2 = rng(0)
+
+    n_resamples = 10
+    shape = 3, 4, 5, 6
+
+    np.random.seed(0)
+    x = np.random.rand(*shape)
+    y = _bootstrap._bootstrap_resample(x, n_resamples, random_state=rng1)
+
+    for i in range(n_resamples):
+        # each resample is indexed along second to last axis
+        # (last axis is the one the statistic will be taken over / consumed)
+        slc = y[..., i, :]
+
+        js = rng_integers(rng2, 0, shape[-1], shape[-1])
+        expected = x[..., js]
+
+        assert np.array_equal(slc, expected)
+
+
+@pytest.mark.parametrize("score", [0, 0.5, 1])
+@pytest.mark.parametrize("axis", [0, 1, 2])
+def test_percentile_of_score(score, axis):
+    shape = 10, 20, 30
+    np.random.seed(0)
+    x = np.random.rand(*shape)
+    p = _bootstrap._percentile_of_score(x, score, axis=-1)
+
+    def vectorized_pos(a, score, axis):
+        return np.apply_along_axis(stats.percentileofscore, axis, a, score)
+
+    p2 = vectorized_pos(x, score, axis=-1)/100
+
+    assert_allclose(p, p2, 1e-15)
+
+
+def test_percentile_along_axis():
+    # the difference between _percentile_along_axis and np.percentile is that
+    # np.percentile gets _all_ the qs for each axis slice, whereas
+    # _percentile_along_axis gets the q corresponding with each axis slice
+
+    shape = 10, 20
+    np.random.seed(0)
+    x = np.random.rand(*shape)
+    q = np.random.rand(*shape[:-1]) * 100
+    y = _bootstrap._percentile_along_axis(x, q)
+
+    for i in range(shape[0]):
+        res = y[i]
+        expected = np.percentile(x[i], q[i], axis=-1)
+        assert_allclose(res, expected, 1e-15)
+
+
+@pytest.mark.parametrize("axis", [0, 1, 2])
+def test_vectorize_statistic(axis):
+    # test that _vectorize_statistic vectorizes a statistic along `axis`
+
+    def statistic(*data, axis):
+        # an arbitrary, vectorized statistic
+        return sum((sample.mean(axis) for sample in data))
+
+    def statistic_1d(*data):
+        # the same statistic, not vectorized
+        for sample in data:
+            assert sample.ndim == 1
+        return statistic(*data, axis=0)
+
+    # vectorize the non-vectorized statistic
+    statistic2 = _bootstrap._vectorize_statistic(statistic_1d)
+
+    np.random.seed(0)
+    x = np.random.rand(4, 5, 6)
+    y = np.random.rand(4, 1, 6)
+    z = np.random.rand(1, 5, 6)
+
+    res1 = statistic(x, y, z, axis=axis)
+    res2 = statistic2(x, y, z, axis=axis)
+    assert_allclose(res1, res2)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_contingency.py

@@ -0,0 +1,234 @@
+import numpy as np
+from numpy.testing import (assert_equal, assert_array_equal,
+                           assert_array_almost_equal, assert_approx_equal,
+                           assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+from scipy.special import xlogy
+from scipy.stats.contingency import (margins, expected_freq,
+                                     chi2_contingency, association)
+
+
+def test_margins():
+    a = np.array([1])
+    m = margins(a)
+    assert_equal(len(m), 1)
+    m0 = m[0]
+    assert_array_equal(m0, np.array([1]))
+
+    a = np.array([[1]])
+    m0, m1 = margins(a)
+    expected0 = np.array([[1]])
+    expected1 = np.array([[1]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(12).reshape(2, 6)
+    m0, m1 = margins(a)
+    expected0 = np.array([[15], [51]])
+    expected1 = np.array([[6, 8, 10, 12, 14, 16]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(24).reshape(2, 3, 4)
+    m0, m1, m2 = margins(a)
+    expected0 = np.array([[[66]], [[210]]])
+    expected1 = np.array([[[60], [92], [124]]])
+    expected2 = np.array([[[60, 66, 72, 78]]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+    assert_array_equal(m2, expected2)
+
+
+def test_expected_freq():
+    assert_array_equal(expected_freq([1]), np.array([1.0]))
+
+    observed = np.array([[[2, 0], [0, 2]], [[0, 2], [2, 0]], [[1, 1], [1, 1]]])
+    e = expected_freq(observed)
+    assert_array_equal(e, np.ones_like(observed))
+
+    observed = np.array([[10, 10, 20], [20, 20, 20]])
+    e = expected_freq(observed)
+    correct = np.array([[12., 12., 16.], [18., 18., 24.]])
+    assert_array_almost_equal(e, correct)
+
+
+def test_chi2_contingency_trivial():
+    # Some very simple tests for chi2_contingency.
+
+    # A trivial case
+    obs = np.array([[1, 2], [1, 2]])
+    chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+    assert_equal(chi2, 0.0)
+    assert_equal(p, 1.0)
+    assert_equal(dof, 1)
+    assert_array_equal(obs, expected)
+
+    # A *really* trivial case: 1-D data.
+    obs = np.array([1, 2, 3])
+    chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+    assert_equal(chi2, 0.0)
+    assert_equal(p, 1.0)
+    assert_equal(dof, 0)
+    assert_array_equal(obs, expected)
+
+
+def test_chi2_contingency_R():
+    # Some test cases that were computed independently, using R.
+
+    # Rcode = \
+    # """
+    # # Data vector.
+    # data <- c(
+    #   12, 34, 23,     4,  47,  11,
+    #   35, 31, 11,    34,  10,  18,
+    #   12, 32,  9,    18,  13,  19,
+    #   12, 12, 14,     9,  33,  25
+    #   )
+    #
+    # # Create factor tags:r=rows, c=columns, t=tiers
+    # r <- factor(gl(4, 2*3, 2*3*4, labels=c("r1", "r2", "r3", "r4")))
+    # c <- factor(gl(3, 1,   2*3*4, labels=c("c1", "c2", "c3")))
+    # t <- factor(gl(2, 3,   2*3*4, labels=c("t1", "t2")))
+    #
+    # # 3-way Chi squared test of independence
+    # s = summary(xtabs(data~r+c+t))
+    # print(s)
+    # """
+    # Routput = \
+    # """
+    # Call: xtabs(formula = data ~ r + c + t)
+    # Number of cases in table: 478
+    # Number of factors: 3
+    # Test for independence of all factors:
+    #         Chisq = 102.17, df = 17, p-value = 3.514e-14
+    # """
+    obs = np.array(
+        [[[12, 34, 23],
+          [35, 31, 11],
+          [12, 32, 9],
+          [12, 12, 14]],
+         [[4, 47, 11],
+          [34, 10, 18],
+          [18, 13, 19],
+          [9, 33, 25]]])
+    chi2, p, dof, expected = chi2_contingency(obs)
+    assert_approx_equal(chi2, 102.17, significant=5)
+    assert_approx_equal(p, 3.514e-14, significant=4)
+    assert_equal(dof, 17)
+
+    # Rcode = \
+    # """
+    # # Data vector.
+    # data <- c(
+    #     #
+    #     12, 17,
+    #     11, 16,
+    #     #
+    #     11, 12,
+    #     15, 16,
+    #     #
+    #     23, 15,
+    #     30, 22,
+    #     #
+    #     14, 17,
+    #     15, 16
+    #     )
+    #
+    # # Create factor tags:r=rows, c=columns, d=depths(?), t=tiers
+    # r <- factor(gl(2, 2,  2*2*2*2, labels=c("r1", "r2")))
+    # c <- factor(gl(2, 1,  2*2*2*2, labels=c("c1", "c2")))
+    # d <- factor(gl(2, 4,  2*2*2*2, labels=c("d1", "d2")))
+    # t <- factor(gl(2, 8,  2*2*2*2, labels=c("t1", "t2")))
+    #
+    # # 4-way Chi squared test of independence
+    # s = summary(xtabs(data~r+c+d+t))
+    # print(s)
+    # """
+    # Routput = \
+    # """
+    # Call: xtabs(formula = data ~ r + c + d + t)
+    # Number of cases in table: 262
+    # Number of factors: 4
+    # Test for independence of all factors:
+    #         Chisq = 8.758, df = 11, p-value = 0.6442
+    # """
+    obs = np.array(
+        [[[[12, 17],
+           [11, 16]],
+          [[11, 12],
+           [15, 16]]],
+         [[[23, 15],
+           [30, 22]],
+          [[14, 17],
+           [15, 16]]]])
+    chi2, p, dof, expected = chi2_contingency(obs)
+    assert_approx_equal(chi2, 8.758, significant=4)
+    assert_approx_equal(p, 0.6442, significant=4)
+    assert_equal(dof, 11)
+
+
+def test_chi2_contingency_g():
+    c = np.array([[15, 60], [15, 90]])
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                    correction=False)
+    assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood',
+                                    correction=True)
+    c_corr = c + np.array([[-0.5, 0.5], [0.5, -0.5]])
+    assert_allclose(g, 2*xlogy(c_corr, c_corr/e).sum())
+
+    c = np.array([[10, 12, 10], [12, 10, 10]])
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood')
+    assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+
+def test_chi2_contingency_bad_args():
+    # Test that "bad" inputs raise a ValueError.
+
+    # Negative value in the array of observed frequencies.
+    obs = np.array([[-1, 10], [1, 2]])
+    assert_raises(ValueError, chi2_contingency, obs)
+
+    # The zeros in this will result in zeros in the array
+    # of expected frequencies.
+    obs = np.array([[0, 1], [0, 1]])
+    assert_raises(ValueError, chi2_contingency, obs)
+
+    # A degenerate case: `observed` has size 0.
+    obs = np.empty((0, 8))
+    assert_raises(ValueError, chi2_contingency, obs)
+
+
+def test_chi2_contingency_yates_gh13875():
+    # Magnitude of Yates' continuity correction should not exceed difference
+    # between expected and observed value of the statistic; see gh-13875
+    observed = np.array([[1573, 3], [4, 0]])
+    p = chi2_contingency(observed)[1]
+    assert_allclose(p, 1, rtol=1e-12)
+
+
+def test_bad_association_args():
+    # Invalid Test Statistic
+    assert_raises(ValueError, association, [[1, 2], [3, 4]], "X")
+    # Invalid array shape
+    assert_raises(ValueError, association, [[[1, 2]], [[3, 4]]], "cramer")
+    # chi2_contingency exception
+    assert_raises(ValueError, association, [[-1, 10], [1, 2]], 'cramer')
+    # Invalid Array Item Data Type
+    assert_raises(ValueError, association,
+                  np.array([[1, 2], ["dd", 4]], dtype=object), 'cramer')
+
+
+@pytest.mark.parametrize('stat, expected',
+                         [('cramer', 0.09222412010290792),
+                          ('tschuprow', 0.0775509319944633),
+                          ('pearson', 0.12932925727138758)])
+def test_assoc(stat, expected):
+    # 2d Array
+    obs1 = np.array([[12, 13, 14, 15, 16],
+                     [17, 16, 18, 19, 11],
+                     [9, 15, 14, 12, 11]])
+    a = association(observed=obs1, method=stat)
+    assert_allclose(a, expected)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_continuous_basic.py

@@ -0,0 +1,834 @@
+
+import numpy as np
+import numpy.testing as npt
+import pytest
+from pytest import raises as assert_raises
+from scipy.integrate import IntegrationWarning
+
+from scipy import stats
+from scipy.special import betainc
+from .common_tests import (check_normalization, check_moment, check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_entropy_vect_scale,
+                           check_edge_support, check_named_args,
+                           check_random_state_property,
+                           check_meth_dtype, check_ppf_dtype, check_cmplx_deriv,
+                           check_pickling, check_rvs_broadcast, check_freezing)
+from scipy.stats._distr_params import distcont
+
+"""
+Test all continuous distributions.
+
+Parameters were chosen for those distributions that pass the
+Kolmogorov-Smirnov test.  This provides safe parameters for each
+distributions so that we can perform further testing of class methods.
+
+These tests currently check only/mostly for serious errors and exceptions,
+not for numerically exact results.
+"""
+
+# Note that you need to add new distributions you want tested
+# to _distr_params
+
+DECIMAL = 5  # specify the precision of the tests  # increased from 0 to 5
+
+distslow = ['kstwo', 'genexpon', 'ksone', 'recipinvgauss', 'vonmises',
+            'kappa4', 'vonmises_line', 'gausshyper', 'norminvgauss',
+            'geninvgauss', 'genhyperbolic']
+# distslow are sorted by speed (very slow to slow)
+
+distxslow = ['studentized_range']
+# distxslow are sorted by speed (very slow to slow)
+
+# skip check_fit_args (test is slow)
+skip_fit_test_mle = ['exponpow', 'exponweib', 'gausshyper', 'genexpon',
+                     'halfgennorm', 'gompertz', 'johnsonsb', 'johnsonsu',
+                     'kappa4', 'ksone', 'kstwo', 'kstwobign', 'mielke', 'ncf',
+                     'nct', 'powerlognorm', 'powernorm', 'recipinvgauss',
+                     'trapezoid', 'vonmises', 'vonmises_line', 'levy_stable',
+                     'rv_histogram_instance', 'studentized_range']
+
+# these were really slow in `test_fit`.py.
+# note that this list is used to skip both fit_test and fit_fix tests
+slow_fit_test_mm = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
+                    'genhalflogistic', 'halfgennorm', 'gompertz', 'johnsonsb',
+                    'kappa4', 'kstwobign', 'recipinvgauss', 'skewnorm',
+                    'trapezoid', 'truncexpon', 'vonmises', 'vonmises_line',
+                    'studentized_range']
+# pearson3 fails due to something weird
+# the first list fails due to non-finite distribution moments encountered
+# most of the rest fail due to integration warnings
+# pearson3 is overriden as not implemented due to gh-11746
+fail_fit_test_mm = (['alpha', 'betaprime', 'bradford', 'burr', 'burr12',
+                     'cauchy', 'crystalball', 'f', 'fisk', 'foldcauchy',
+                     'genextreme', 'genpareto', 'halfcauchy', 'invgamma',
+                     'kappa3', 'levy', 'levy_l', 'loglaplace', 'lomax',
+                     'mielke', 'nakagami', 'ncf', 'skewcauchy', 't',
+                     'tukeylambda', 'invweibull']
+                     + ['genhyperbolic', 'johnsonsu', 'ksone', 'kstwo',
+                        'nct', 'pareto', 'powernorm', 'powerlognorm']
+                     + ['pearson3'])
+skip_fit_test = {"MLE": skip_fit_test_mle,
+                 "MM": slow_fit_test_mm + fail_fit_test_mm}
+
+# skip check_fit_args_fix (test is slow)
+skip_fit_fix_test_mle = ['burr', 'exponpow', 'exponweib', 'gausshyper',
+                         'genexpon', 'halfgennorm', 'gompertz', 'johnsonsb',
+                         'johnsonsu', 'kappa4', 'ksone', 'kstwo', 'kstwobign',
+                         'levy_stable', 'mielke', 'ncf', 'ncx2',
+                         'powerlognorm', 'powernorm', 'rdist', 'recipinvgauss',
+                         'trapezoid', 'vonmises', 'vonmises_line',
+                         'studentized_range']
+# the first list fails due to non-finite distribution moments encountered
+# most of the rest fail due to integration warnings
+# pearson3 is overriden as not implemented due to gh-11746
+fail_fit_fix_test_mm = (['alpha', 'betaprime', 'burr', 'burr12', 'cauchy',
+                         'crystalball', 'f', 'fisk', 'foldcauchy',
+                         'genextreme', 'genpareto', 'halfcauchy', 'invgamma',
+                         'kappa3', 'levy', 'levy_l', 'loglaplace', 'lomax',
+                         'mielke', 'nakagami', 'ncf', 'nct', 'skewcauchy', 't',
+                         'invweibull']
+                         + ['genhyperbolic', 'johnsonsu', 'ksone', 'kstwo',
+                            'pareto', 'powernorm', 'powerlognorm']
+                         + ['pearson3'])
+skip_fit_fix_test = {"MLE": skip_fit_fix_test_mle,
+                     "MM": slow_fit_test_mm + fail_fit_fix_test_mm}
+
+# These distributions fail the complex derivative test below.
+# Here 'fail' mean produce wrong results and/or raise exceptions, depending
+# on the implementation details of corresponding special functions.
+# cf https://github.com/scipy/scipy/pull/4979 for a discussion.
+fails_cmplx = set(['argus', 'beta', 'betaprime', 'chi', 'chi2', 'cosine',
+                   'dgamma', 'dweibull', 'erlang', 'f', 'gamma',
+                   'gausshyper', 'gengamma', 'genhyperbolic',
+                   'geninvgauss', 'gennorm', 'genpareto',
+                   'halfgennorm', 'invgamma',
+                   'ksone', 'kstwo', 'kstwobign', 'levy_l', 'loggamma',
+                   'logistic', 'loguniform', 'maxwell', 'nakagami',
+                   'ncf', 'nct', 'ncx2', 'norminvgauss', 'pearson3', 'rdist',
+                   'reciprocal', 'rice', 'skewnorm', 't', 'tukeylambda',
+                   'vonmises', 'vonmises_line', 'rv_histogram_instance',
+                   'truncnorm', 'studentized_range'])
+
+_h = np.histogram([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
+                   6, 6, 6, 7, 7, 7, 8, 8, 9], bins=8)
+histogram_test_instance = stats.rv_histogram(_h)
+
+
+def cases_test_cont_basic():
+    for distname, arg in distcont[:] + [(histogram_test_instance, tuple())]:
+        if distname == 'levy_stable':
+            continue
+        elif distname in distslow:
+            yield pytest.param(distname, arg, marks=pytest.mark.slow)
+        elif distname in distxslow:
+            yield pytest.param(distname, arg, marks=pytest.mark.xslow)
+        else:
+            yield distname, arg
+
+
+@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
+@pytest.mark.parametrize('sn, n_fit_samples', [(500, 200)])
+def test_cont_basic(distname, arg, sn, n_fit_samples):
+    # this test skips slow distributions
+
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    rng = np.random.RandomState(765456)
+    rvs = distfn.rvs(size=sn, *arg, random_state=rng)
+    sm = rvs.mean()
+    sv = rvs.var()
+    m, v = distfn.stats(*arg)
+
+    check_sample_meanvar_(distfn, arg, m, v, sm, sv, sn, distname + 'sample mean test')
+    check_cdf_ppf(distfn, arg, distname)
+    check_sf_isf(distfn, arg, distname)
+    check_pdf(distfn, arg, distname)
+    check_pdf_logpdf(distfn, arg, distname)
+    check_pdf_logpdf_at_endpoints(distfn, arg, distname)
+    check_cdf_logcdf(distfn, arg, distname)
+    check_sf_logsf(distfn, arg, distname)
+    check_ppf_broadcast(distfn, arg, distname)
+
+    alpha = 0.01
+    if distname == 'rv_histogram_instance':
+        check_distribution_rvs(distfn.cdf, arg, alpha, rvs)
+    elif distname != 'geninvgauss':
+        # skip kstest for geninvgauss since cdf is too slow; see test for
+        # rv generation in TestGenInvGauss in test_distributions.py
+        check_distribution_rvs(distname, arg, alpha, rvs)
+
+    locscale_defaults = (0, 1)
+    meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
+             distfn.logsf]
+    # make sure arguments are within support
+    spec_x = {'weibull_max': -0.5, 'levy_l': -0.5,
+              'pareto': 1.5, 'tukeylambda': 0.3,
+              'rv_histogram_instance': 5.0}
+    x = spec_x.get(distname, 0.5)
+    if distname == 'invweibull':
+        arg = (1,)
+    elif distname == 'ksone':
+        arg = (3,)
+
+    check_named_args(distfn, x, arg, locscale_defaults, meths)
+    check_random_state_property(distfn, arg)
+    check_pickling(distfn, arg)
+    check_freezing(distfn, arg)
+
+    # Entropy
+    if distname not in ['kstwobign', 'kstwo']:
+        check_entropy(distfn, arg, distname)
+
+    if distfn.numargs == 0:
+        check_vecentropy(distfn, arg)
+
+    if (distfn.__class__._entropy != stats.rv_continuous._entropy
+            and distname != 'vonmises'):
+        check_private_entropy(distfn, arg, stats.rv_continuous)
+
+    with npt.suppress_warnings() as sup:
+        sup.filter(IntegrationWarning, "The occurrence of roundoff error")
+        sup.filter(IntegrationWarning, "Extremely bad integrand")
+        sup.filter(RuntimeWarning, "invalid value")
+        check_entropy_vect_scale(distfn, arg)
+
+    check_retrieving_support(distfn, arg)
+    check_edge_support(distfn, arg)
+
+    check_meth_dtype(distfn, arg, meths)
+    check_ppf_dtype(distfn, arg)
+
+    if distname not in fails_cmplx:
+        check_cmplx_deriv(distfn, arg)
+
+    if distname != 'truncnorm':
+        check_ppf_private(distfn, arg, distname)
+
+    for method in ["MLE", "MM"]:
+        if distname not in skip_fit_test[method]:
+            check_fit_args(distfn, arg, rvs[:n_fit_samples], method)
+
+        if distname not in skip_fit_fix_test[method]:
+            check_fit_args_fix(distfn, arg, rvs[:n_fit_samples], method)
+
+
+@pytest.mark.parametrize('distname,arg', cases_test_cont_basic())
+def test_rvs_scalar(distname, arg):
+    # rvs should return a scalar when given scalar arguments (gh-12428)
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    assert np.isscalar(distfn.rvs(*arg))
+    assert np.isscalar(distfn.rvs(*arg, size=()))
+    assert np.isscalar(distfn.rvs(*arg, size=None))
+
+
+def test_levy_stable_random_state_property():
+    # levy_stable only implements rvs(), so it is skipped in the
+    # main loop in test_cont_basic(). Here we apply just the test
+    # check_random_state_property to levy_stable.
+    check_random_state_property(stats.levy_stable, (0.5, 0.1))
+
+
+def cases_test_moments():
+    fail_normalization = set(['vonmises'])
+    fail_higher = set(['vonmises', 'ncf'])
+    fail_loc_scale = set(['kappa3', 'kappa4'])  # see gh-13582
+
+    for distname, arg in distcont[:] + [(histogram_test_instance, tuple())]:
+        if distname == 'levy_stable':
+            continue
+
+        if distname == 'studentized_range':
+            msg = ("studentized_range is far too slow for this test and it is "
+                   "redundant with test_distributions::TestStudentizedRange::"
+                   "test_moment_against_mp")
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=pytest.mark.xslow(reason=msg))
+            continue
+        cond1 = distname not in fail_normalization
+        cond2 = distname not in fail_higher
+        cond3 = distname not in fail_loc_scale
+
+        yield distname, arg, cond1, cond2, cond3, False
+
+        if not cond1 or not cond2 or not cond3:
+            # Run the distributions that have issues twice, once skipping the
+            # not_ok parts, once with the not_ok parts but marked as knownfail
+            yield pytest.param(distname, arg, True, True, True, True,
+                               marks=pytest.mark.xfail)
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg,normalization_ok,higher_ok,'
+                         'loc_scale_ok,is_xfailing',
+                         cases_test_moments())
+def test_moments(distname, arg, normalization_ok, higher_ok, loc_scale_ok,
+                 is_xfailing):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'rv_histogram_instance'
+
+    with npt.suppress_warnings() as sup:
+        sup.filter(IntegrationWarning,
+                   "The integral is probably divergent, or slowly convergent.")
+        if is_xfailing:
+            sup.filter(IntegrationWarning)
+
+        m, v, s, k = distfn.stats(*arg, moments='mvsk')
+
+        if normalization_ok:
+            check_normalization(distfn, arg, distname)
+
+        if higher_ok:
+            check_mean_expect(distfn, arg, m, distname)
+            check_skew_expect(distfn, arg, m, v, s, distname)
+            check_var_expect(distfn, arg, m, v, distname)
+            check_kurt_expect(distfn, arg, m, v, k, distname)
+
+        if loc_scale_ok:
+            check_loc_scale(distfn, arg, m, v, distname)
+
+        check_moment(distfn, arg, m, v, distname)
+
+
+@pytest.mark.parametrize('dist,shape_args', distcont)
+def test_rvs_broadcast(dist, shape_args):
+    if dist in ['gausshyper', 'genexpon', 'studentized_range']:
+        pytest.skip("too slow")
+
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['argus', 'betaprime', 'dgamma', 'dweibull',
+                          'exponnorm', 'genhyperbolic', 'geninvgauss',
+                          'levy_stable', 'nct', 'norminvgauss', 'rice',
+                          'skewnorm', 'semicircular']
+
+    distfunc = getattr(stats, dist)
+    loc = np.zeros(2)
+    scale = np.ones((3, 1))
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = [3, 2]
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 4,) + (1,)*(k + 2)
+        allargs.append(shape_args[k]*np.ones(shp))
+        bshape.insert(0, k + 4)
+    allargs.extend([loc, scale])
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+
+    check_rvs_broadcast(distfunc, dist, allargs, bshape, shape_only, 'd')
+
+
+def test_rvs_gh2069_regression():
+    # Regression tests for gh-2069.  In scipy 0.17 and earlier,
+    # these tests would fail.
+    #
+    # A typical example of the broken behavior:
+    # >>> norm.rvs(loc=np.zeros(5), scale=np.ones(5))
+    # array([-2.49613705, -2.49613705, -2.49613705, -2.49613705, -2.49613705])
+    rng = np.random.RandomState(123)
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=1, random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=0, scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.zeros(5), scale=np.ones(5), random_state=rng)
+    d = np.diff(vals)
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+    vals = stats.norm.rvs(loc=np.array([[0], [0]]), scale=np.ones(5),
+                          random_state=rng)
+    d = np.diff(vals.ravel())
+    npt.assert_(np.all(d != 0), "All the values are equal, but they shouldn't be!")
+
+    assert_raises(ValueError, stats.norm.rvs, [[0, 0], [0, 0]],
+                  [[1, 1], [1, 1]], 1)
+    assert_raises(ValueError, stats.gamma.rvs, [2, 3, 4, 5], 0, 1, (2, 2))
+    assert_raises(ValueError, stats.gamma.rvs, [1, 1, 1, 1], [0, 0, 0, 0],
+                     [[1], [2]], (4,))
+
+
+def test_nomodify_gh9900_regression():
+    # Regression test for gh-9990
+    # Prior to gh-9990, calls to stats.truncnorm._cdf() use what ever was
+    # set inside the stats.truncnorm instance during stats.truncnorm.cdf().
+    # This could cause issues wth multi-threaded code.
+    # Since then, the calls to cdf() are not permitted to modify the global
+    # stats.truncnorm instance.
+    tn = stats.truncnorm
+    # Use the right-half truncated normal
+    # Check that the cdf and _cdf return the same result.
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf), 0.6826894921370859)
+    npt.assert_almost_equal(tn._cdf(1, 0, np.inf), 0.6826894921370859)
+
+    # Now use the left-half truncated normal
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0), 0.31731050786291415)
+    npt.assert_almost_equal(tn._cdf(-1, -np.inf, 0), 0.31731050786291415)
+
+    # Check that the right-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf(1, 0, np.inf), 0.6826894921370859)  # NOT 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, 0, np.inf), 0.6826894921370859)
+
+    # Check that the left-half truncated normal _cdf hasn't changed
+    npt.assert_almost_equal(tn._cdf(-1, -np.inf, 0), 0.31731050786291415)  # Not -0.6826894921370859
+    npt.assert_almost_equal(tn.cdf(1, -np.inf, 0), 1)                     # Not 1.6826894921370859
+    npt.assert_almost_equal(tn.cdf(-1, -np.inf, 0), 0.31731050786291415)  # Not -0.6826894921370859
+
+
+def test_broadcast_gh9990_regression():
+    # Regression test for gh-9990
+    # The x-value 7 only lies within the support of 4 of the supplied
+    # distributions.  Prior to 9990, one array passed to
+    # stats.reciprocal._cdf would have 4 elements, but an array
+    # previously stored by stats.reciprocal_argcheck() would have 6, leading
+    # to a broadcast error.
+    a = np.array([1, 2, 3, 4, 5, 6])
+    b = np.array([8, 16, 1, 32, 1, 48])
+    ans = [stats.reciprocal.cdf(7, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(7, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(1, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(1, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_a, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(a, a, b), ans)
+
+    ans = [stats.reciprocal.cdf(_b, _a, _b) for _a, _b in zip(a,b)]
+    npt.assert_array_almost_equal(stats.reciprocal.cdf(b, a, b), ans)
+
+
+def test_broadcast_gh7933_regression():
+    # Check broadcast works
+    stats.truncnorm.logpdf(
+        np.array([3.0, 2.0, 1.0]),
+        a=(1.5 - np.array([6.0, 5.0, 4.0])) / 3.0,
+        b=np.inf,
+        loc=np.array([6.0, 5.0, 4.0]),
+        scale=3.0
+    )
+
+
+def test_gh2002_regression():
+    # Add a check that broadcast works in situations where only some
+    # x-values are compatible with some of the shape arguments.
+    x = np.r_[-2:2:101j]
+    a = np.r_[-np.ones(50), np.ones(51)]
+    expected = [stats.truncnorm.pdf(_x, _a, np.inf) for _x, _a in zip(x, a)]
+    ans = stats.truncnorm.pdf(x, a, np.inf)
+    npt.assert_array_almost_equal(ans, expected)
+
+
+def test_gh1320_regression():
+    # Check that the first example from gh-1320 now works.
+    c = 2.62
+    stats.genextreme.ppf(0.5, np.array([[c], [c + 0.5]]))
+    # The other examples in gh-1320 appear to have stopped working
+    # some time ago.
+    # ans = stats.genextreme.moment(2, np.array([c, c + 0.5]))
+    # expected = np.array([25.50105963, 115.11191437])
+    # stats.genextreme.moment(5, np.array([[c], [c + 0.5]]))
+    # stats.genextreme.moment(5, np.array([c, c + 0.5]))
+
+
+def test_method_of_moments():
+    # example from https://en.wikipedia.org/wiki/Method_of_moments_(statistics)
+    np.random.seed(1234)
+    x = [0, 0, 0, 0, 1]
+    a = 1/5 - 2*np.sqrt(3)/5
+    b = 1/5 + 2*np.sqrt(3)/5
+    # force use of method of moments (uniform.fit is overriden)
+    loc, scale = super(type(stats.uniform), stats.uniform).fit(x, method="MM")
+    npt.assert_almost_equal(loc, a, decimal=4)
+    npt.assert_almost_equal(loc+scale, b, decimal=4)
+
+
+def check_sample_meanvar_(distfn, arg, m, v, sm, sv, sn, msg):
+    # this did not work, skipped silently by nose
+    if np.isfinite(m):
+        check_sample_mean(sm, sv, sn, m)
+    if np.isfinite(v):
+        check_sample_var(sv, sn, v)
+
+
+def check_sample_mean(sm, v, n, popmean):
+    # from stats._stats_py.ttest_1samp(a, popmean):
+    # Calculates the t-obtained for the independent samples T-test on ONE group
+    # of scores a, given a population mean.
+    #
+    # Returns: t-value, two-tailed prob
+    df = n-1
+    svar = ((n-1)*v) / float(df)    # looks redundant
+    t = (sm-popmean) / np.sqrt(svar*(1.0/n))
+    prob = betainc(0.5*df, 0.5, df/(df + t*t))
+
+    # return t,prob
+    npt.assert_(prob > 0.01, 'mean fail, t,prob = %f, %f, m, sm=%f,%f' %
+                (t, prob, popmean, sm))
+
+
+def check_sample_var(sv, n, popvar):
+    # two-sided chisquare test for sample variance equal to
+    # hypothesized variance
+    df = n-1
+    chi2 = (n - 1)*sv/popvar
+    pval = stats.distributions.chi2.sf(chi2, df) * 2
+    npt.assert_(pval > 0.01, 'var fail, t, pval = %f, %f, v, sv=%f, %f' %
+                (chi2, pval, popvar, sv))
+
+
+def check_cdf_ppf(distfn, arg, msg):
+    values = [0.001, 0.5, 0.999]
+    npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg),
+                            values, decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-ppf roundtrip')
+
+
+def check_sf_isf(distfn, arg, msg):
+    npt.assert_almost_equal(distfn.sf(distfn.isf([0.1, 0.5, 0.9], *arg), *arg),
+                            [0.1, 0.5, 0.9], decimal=DECIMAL, err_msg=msg +
+                            ' - sf-isf roundtrip')
+    npt.assert_almost_equal(distfn.cdf([0.1, 0.9], *arg),
+                            1.0 - distfn.sf([0.1, 0.9], *arg),
+                            decimal=DECIMAL, err_msg=msg +
+                            ' - cdf-sf relationship')
+
+
+def check_pdf(distfn, arg, msg):
+    # compares pdf at median with numerical derivative of cdf
+    median = distfn.ppf(0.5, *arg)
+    eps = 1e-6
+    pdfv = distfn.pdf(median, *arg)
+    if (pdfv < 1e-4) or (pdfv > 1e4):
+        # avoid checking a case where pdf is close to zero or
+        # huge (singularity)
+        median = median + 0.1
+        pdfv = distfn.pdf(median, *arg)
+    cdfdiff = (distfn.cdf(median + eps, *arg) -
+               distfn.cdf(median - eps, *arg))/eps/2.0
+    # replace with better diff and better test (more points),
+    # actually, this works pretty well
+    msg += ' - cdf-pdf relationship'
+    npt.assert_almost_equal(pdfv, cdfdiff, decimal=DECIMAL, err_msg=msg)
+
+
+def check_pdf_logpdf(distfn, args, msg):
+    # compares pdf at several points with the log of the pdf
+    points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    pdf = distfn.pdf(vals, *args)
+    logpdf = distfn.logpdf(vals, *args)
+    pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+    logpdf = logpdf[np.isfinite(logpdf)]
+    msg += " - logpdf-log(pdf) relationship"
+    npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_pdf_logpdf_at_endpoints(distfn, args, msg):
+    # compares pdf with the log of the pdf at the (finite) end points
+    points = np.array([0, 1])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    with npt.suppress_warnings() as sup:
+        # Several distributions incur divide by zero or encounter invalid values when computing
+        # the pdf or logpdf at the endpoints.
+        suppress_messsages = [
+            "divide by zero encountered in true_divide",  # multiple distributions
+            "divide by zero encountered in log",  # multiple distributions
+            "divide by zero encountered in power",  # gengamma
+            "invalid value encountered in add",  # genextreme
+            "invalid value encountered in subtract",  # gengamma
+            ]
+        for msg in suppress_messsages:
+            sup.filter(category=RuntimeWarning, message=msg)
+
+        pdf = distfn.pdf(vals, *args)
+        logpdf = distfn.logpdf(vals, *args)
+        pdf = pdf[(pdf != 0) & np.isfinite(pdf)]
+        logpdf = logpdf[np.isfinite(logpdf)]
+        msg += " - logpdf-log(pdf) relationship"
+        npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg)
+
+
+def check_sf_logsf(distfn, args, msg):
+    # compares sf at several points with the log of the sf
+    points = np.array([0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    sf = distfn.sf(vals, *args)
+    logsf = distfn.logsf(vals, *args)
+    sf = sf[sf != 0]
+    logsf = logsf[np.isfinite(logsf)]
+    msg += " - logsf-log(sf) relationship"
+    npt.assert_almost_equal(np.log(sf), logsf, decimal=7, err_msg=msg)
+
+
+def check_cdf_logcdf(distfn, args, msg):
+    # compares cdf at several points with the log of the cdf
+    points = np.array([0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 1.0])
+    vals = distfn.ppf(points, *args)
+    vals = vals[np.isfinite(vals)]
+    cdf = distfn.cdf(vals, *args)
+    logcdf = distfn.logcdf(vals, *args)
+    cdf = cdf[cdf != 0]
+    logcdf = logcdf[np.isfinite(logcdf)]
+    msg += " - logcdf-log(cdf) relationship"
+    npt.assert_almost_equal(np.log(cdf), logcdf, decimal=7, err_msg=msg)
+
+
+def check_ppf_broadcast(distfn, arg, msg):
+    # compares ppf for multiple argsets.
+    num_repeats = 5
+    args = [] * num_repeats
+    if arg:
+        args = [np.array([_] * num_repeats) for _ in arg]
+
+    median = distfn.ppf(0.5, *arg)
+    medians = distfn.ppf(0.5, *args)
+    msg += " - ppf multiple"
+    npt.assert_almost_equal(medians, [median] * num_repeats, decimal=7, err_msg=msg)
+
+
+def check_distribution_rvs(dist, args, alpha, rvs):
+    # dist is either a cdf function or name of a distribution in scipy.stats.
+    # args are the args for scipy.stats.dist(*args)
+    # alpha is a significance level, ~0.01
+    # rvs is array_like of random variables
+    # test from scipy.stats.tests
+    # this version reuses existing random variables
+    D, pval = stats.kstest(rvs, dist, args=args, N=1000)
+    if (pval < alpha):
+        # The rvs passed in failed the K-S test, which _could_ happen
+        # but is unlikely if alpha is small enough.
+        # Repeat the the test with a new sample of rvs.
+        # Generate 1000 rvs, perform a K-S test that the new sample of rvs
+        # are distributed according to the distribution.
+        D, pval = stats.kstest(dist, dist, args=args, N=1000)
+        npt.assert_(pval > alpha, "D = " + str(D) + "; pval = " + str(pval) +
+                    "; alpha = " + str(alpha) + "\nargs = " + str(args))
+
+
+def check_vecentropy(distfn, args):
+    npt.assert_equal(distfn.vecentropy(*args), distfn._entropy(*args))
+
+
+def check_loc_scale(distfn, arg, m, v, msg):
+    # Make `loc` and `scale` arrays to catch bugs like gh-13580 where
+    # `loc` and `scale` arrays improperly broadcast with shapes.
+    loc, scale = np.array([10.0, 20.0]), np.array([10.0, 20.0])
+    mt, vt = distfn.stats(loc=loc, scale=scale, *arg)
+    npt.assert_allclose(m*scale + loc, mt)
+    npt.assert_allclose(v*scale*scale, vt)
+
+
+def check_ppf_private(distfn, arg, msg):
+    # fails by design for truncnorm self.nb not defined
+    ppfs = distfn._ppf(np.array([0.1, 0.5, 0.9]), *arg)
+    npt.assert_(not np.any(np.isnan(ppfs)), msg + 'ppf private is nan')
+
+
+def check_retrieving_support(distfn, args):
+    loc, scale = 1, 2
+    supp = distfn.support(*args)
+    supp_loc_scale = distfn.support(*args, loc=loc, scale=scale)
+    npt.assert_almost_equal(np.array(supp)*scale + loc,
+                            np.array(supp_loc_scale))
+
+
+def check_fit_args(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), npt.suppress_warnings() as sup:
+        sup.filter(category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+        sup.filter(category=RuntimeWarning,
+                   message="floating point number truncated")
+        vals = distfn.fit(rvs, method=method)
+        vals2 = distfn.fit(rvs, optimizer='powell', method=method)
+    # Only check the length of the return; accuracy tested in test_fit.py
+    npt.assert_(len(vals) == 2+len(arg))
+    npt.assert_(len(vals2) == 2+len(arg))
+
+
+def check_fit_args_fix(distfn, arg, rvs, method):
+    with np.errstate(all='ignore'), npt.suppress_warnings() as sup:
+        sup.filter(category=RuntimeWarning,
+                   message="The shape parameter of the erlang")
+
+        vals = distfn.fit(rvs, floc=0, method=method)
+        vals2 = distfn.fit(rvs, fscale=1, method=method)
+        npt.assert_(len(vals) == 2+len(arg))
+        npt.assert_(vals[-2] == 0)
+        npt.assert_(vals2[-1] == 1)
+        npt.assert_(len(vals2) == 2+len(arg))
+        if len(arg) > 0:
+            vals3 = distfn.fit(rvs, f0=arg[0], method=method)
+            npt.assert_(len(vals3) == 2+len(arg))
+            npt.assert_(vals3[0] == arg[0])
+        if len(arg) > 1:
+            vals4 = distfn.fit(rvs, f1=arg[1], method=method)
+            npt.assert_(len(vals4) == 2+len(arg))
+            npt.assert_(vals4[1] == arg[1])
+        if len(arg) > 2:
+            vals5 = distfn.fit(rvs, f2=arg[2], method=method)
+            npt.assert_(len(vals5) == 2+len(arg))
+            npt.assert_(vals5[2] == arg[2])
+
+
+@pytest.mark.parametrize('method', ['pdf', 'logpdf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', distcont)
+def test_methods_with_lists(method, distname, args):
+    # Test that the continuous distributions can accept Python lists
+    # as arguments.
+    dist = getattr(stats, distname)
+    f = getattr(dist, method)
+    if distname == 'invweibull' and method.startswith('log'):
+        x = [1.5, 2]
+    else:
+        x = [0.1, 0.2]
+
+    shape2 = [[a]*2 for a in args]
+    loc = [0, 0.1]
+    scale = [1, 1.01]
+    result = f(x, *shape2, loc=loc, scale=scale)
+    npt.assert_allclose(result,
+                        [f(*v) for v in zip(x, *shape2, loc, scale)],
+                        rtol=1e-14, atol=5e-14)
+
+
+def test_burr_fisk_moment_gh13234_regression():
+    vals0 = stats.burr.moment(1, 5, 4)
+    assert isinstance(vals0, float)
+
+    vals1 = stats.fisk.moment(1, 8)
+    assert isinstance(vals1, float)
+
+
+def test_moments_with_array_gh12192_regression():
+    # array loc and scalar scale
+    vals0 = stats.norm.moment(n=1, loc=np.array([1, 2, 3]), scale=1)
+    expected0 = np.array([1., 2., 3.])
+    npt.assert_equal(vals0, expected0)
+
+    # array loc and invalid scalar scale
+    vals1 = stats.norm.moment(n=1, loc=np.array([1, 2, 3]), scale=-1)
+    expected1 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals1, expected1)
+
+    # array loc and array scale with invalid entries
+    vals2 = stats.norm.moment(n=1, loc=np.array([1, 2, 3]), scale=[-3, 1, 0])
+    expected2 = np.array([np.nan, 2., np.nan])
+    npt.assert_equal(vals2, expected2)
+
+    # (loc == 0) & (scale < 0)
+    vals3 = stats.norm.moment(n=2, loc=0, scale=-4)
+    expected3 = np.nan
+    npt.assert_equal(vals3, expected3)
+    assert isinstance(vals3, expected3.__class__)
+
+    # array loc with 0 entries and scale with invalid entries
+    vals4 = stats.norm.moment(n=2, loc=[1, 0, 2], scale=[3, -4, -5])
+    expected4 = np.array([10., np.nan, np.nan])
+    npt.assert_equal(vals4, expected4)
+
+    # all(loc == 0) & (array scale with invalid entries)
+    vals5 = stats.norm.moment(n=2, loc=[0, 0, 0], scale=[5., -2, 100.])
+    expected5 = np.array([25., np.nan, 10000.])
+    npt.assert_equal(vals5, expected5)
+
+    # all( (loc == 0) & (scale < 0) )
+    vals6 = stats.norm.moment(n=2, loc=[0, 0, 0], scale=[-5., -2, -100.])
+    expected6 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals6, expected6)
+
+    # scalar args, loc, and scale
+    vals7 = stats.chi.moment(n=2, df=1, loc=0, scale=0)
+    expected7 = np.nan
+    npt.assert_equal(vals7, expected7)
+    assert isinstance(vals7, expected7.__class__)
+
+    # array args, scalar loc, and scalar scale
+    vals8 = stats.chi.moment(n=2, df=[1, 2, 3], loc=0, scale=0)
+    expected8 = np.array([np.nan, np.nan, np.nan])
+    npt.assert_equal(vals8, expected8)
+
+    # array args, array loc, and array scale
+    vals9 = stats.chi.moment(n=2, df=[1, 2, 3], loc=[1., 0., 2.],
+                             scale=[1., -3., 0.])
+    expected9 = np.array([3.59576912, np.nan, np.nan])
+    npt.assert_allclose(vals9, expected9, rtol=1e-8)
+
+    # (n > 4), all(loc != 0), and all(scale != 0)
+    vals10 = stats.norm.moment(5, [1., 2.], [1., 2.])
+    expected10 = np.array([26., 832.])
+    npt.assert_allclose(vals10, expected10, rtol=1e-13)
+
+    # test broadcasting and more
+    a = [-1.1, 0, 1, 2.2, np.pi]
+    b = [-1.1, 0, 1, 2.2, np.pi]
+    loc = [-1.1, 0, np.sqrt(2)]
+    scale = [-2.1, 0, 1, 2.2, np.pi]
+
+    a = np.array(a).reshape((-1, 1, 1, 1))
+    b = np.array(b).reshape((-1, 1, 1))
+    loc = np.array(loc).reshape((-1, 1))
+    scale = np.array(scale)
+
+    vals11 = stats.beta.moment(n=2, a=a, b=b, loc=loc, scale=scale)
+
+    a, b, loc, scale = np.broadcast_arrays(a, b, loc, scale)
+
+    for i in np.ndenumerate(a):
+        with np.errstate(invalid='ignore', divide='ignore'):
+            i = i[0]  # just get the index
+            # check against same function with scalar input
+            expected = stats.beta.moment(n=2, a=a[i], b=b[i],
+                                         loc=loc[i], scale=scale[i])
+            np.testing.assert_equal(vals11[i], expected)
+
+
+def test_broadcasting_in_moments_gh12192_regression():
+    vals0 = stats.norm.moment(n=1, loc=np.array([1, 2, 3]), scale=[[1]])
+    expected0 = np.array([[1., 2., 3.]])
+    npt.assert_equal(vals0, expected0)
+    assert vals0.shape == expected0.shape
+
+    vals1 = stats.norm.moment(n=1, loc=np.array([[1], [2], [3]]),
+                              scale=[1, 2, 3])
+    expected1 = np.array([[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]])
+    npt.assert_equal(vals1, expected1)
+    assert vals1.shape == expected1.shape
+
+    vals2 = stats.chi.moment(n=1, df=[1., 2., 3.], loc=0., scale=1.)
+    expected2 = np.array([0.79788456, 1.25331414, 1.59576912])
+    npt.assert_allclose(vals2, expected2, rtol=1e-8)
+    assert vals2.shape == expected2.shape
+
+    vals3 = stats.chi.moment(n=1, df=[[1.], [2.], [3.]], loc=[0., 1., 2.],
+                             scale=[-1., 0., 3.])
+    expected3 = np.array([[np.nan, np.nan, 4.39365368],
+                          [np.nan, np.nan, 5.75994241],
+                          [np.nan, np.nan, 6.78730736]])
+    npt.assert_allclose(vals3, expected3, rtol=1e-8)
+    assert vals3.shape == expected3.shape

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_crosstab.py

@@ -0,0 +1,110 @@
+import pytest
+import numpy as np
+from numpy.testing import assert_array_equal
+from scipy.stats.contingency import crosstab
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_basic(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [2, 1, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [1, 2, 3]
+    expected_count = np.array([[1, 2, 1],
+                               [1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.A, expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_crosstab_basic_1d():
+    # Verify that a single input sequence works as expected.
+    x = [1, 2, 3, 1, 2, 3, 3]
+    expected_xvals = [1, 2, 3]
+    expected_count = np.array([2, 2, 3])
+    (xvals,), count = crosstab(x)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(count, expected_count)
+
+
+def test_crosstab_basic_3d():
+    # Verify the function for three input sequences.
+    a = 'a'
+    b = 'b'
+    x = [0, 0, 9, 9, 0, 0, 9, 9]
+    y = [a, a, a, a, b, b, b, a]
+    z = [1, 2, 3, 1, 2, 3, 3, 1]
+    expected_xvals = [0, 9]
+    expected_yvals = [a, b]
+    expected_zvals = [1, 2, 3]
+    expected_count = np.array([[[1, 1, 0],
+                                [0, 1, 1]],
+                               [[2, 0, 1],
+                                [0, 0, 1]]])
+    (xvals, yvals, zvals), count = crosstab(x, y, z)
+    assert_array_equal(xvals, expected_xvals)
+    assert_array_equal(yvals, expected_yvals)
+    assert_array_equal(zvals, expected_zvals)
+    assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_levels(sparse):
+    a = [0, 0, 9, 9, 0, 0, 9]
+    b = [1, 2, 3, 1, 2, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[None, [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.A, expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+@pytest.mark.parametrize('sparse', [False, True])
+def test_crosstab_extra_levels(sparse):
+    # The pair of values (-1, 3) will be ignored, because we explicitly
+    # request the counted `a` values to be [0, 9].
+    a = [0, 0, 9, 9, 0, 0, 9, -1]
+    b = [1, 2, 3, 1, 2, 3, 3, 3]
+    expected_avals = [0, 9]
+    expected_bvals = [0, 1, 2, 3]
+    expected_count = np.array([[0, 1, 2, 1],
+                               [0, 1, 0, 2]])
+    (avals, bvals), count = crosstab(a, b, levels=[[0, 9], [0, 1, 2, 3]],
+                                     sparse=sparse)
+    assert_array_equal(avals, expected_avals)
+    assert_array_equal(bvals, expected_bvals)
+    if sparse:
+        assert_array_equal(count.A, expected_count)
+    else:
+        assert_array_equal(count, expected_count)
+
+
+def test_validation_at_least_one():
+    with pytest.raises(TypeError, match='At least one'):
+        crosstab()
+
+
+def test_validation_same_lengths():
+    with pytest.raises(ValueError, match='must have the same length'):
+        crosstab([1, 2], [1, 2, 3, 4])
+
+
+def test_validation_sparse_only_two_args():
+    with pytest.raises(ValueError, match='only two input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], [1, 3, 3], sparse=True)
+
+
+def test_validation_len_levels_matches_args():
+    with pytest.raises(ValueError, match='number of input sequences'):
+        crosstab([0, 1, 1], [8, 8, 9], levels=([0, 1, 2, 3],))

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_discrete_basic.py

@@ -0,0 +1,317 @@
+import numpy.testing as npt
+import numpy as np
+import pytest
+
+from scipy import stats
+from .common_tests import (check_normalization, check_moment, check_mean_expect,
+                           check_var_expect, check_skew_expect,
+                           check_kurt_expect, check_entropy,
+                           check_private_entropy, check_edge_support,
+                           check_named_args, check_random_state_property,
+                           check_pickling, check_rvs_broadcast, check_freezing)
+from scipy.stats._distr_params import distdiscrete, invdistdiscrete
+
+vals = ([1, 2, 3, 4], [0.1, 0.2, 0.3, 0.4])
+distdiscrete += [[stats.rv_discrete(values=vals), ()]]
+
+# For these distributions, test_discrete_basic only runs with test mode full
+distslow = {'zipfian', 'nhypergeom'}
+
+
+def cases_test_discrete_basic():
+    seen = set()
+    for distname, arg in distdiscrete:
+        if distname in distslow:
+            yield pytest.param(distname, arg, distname, marks=pytest.mark.slow)
+        else:
+            yield distname, arg, distname not in seen
+        seen.add(distname)
+
+
+@pytest.mark.parametrize('distname,arg,first_case', cases_test_discrete_basic())
+def test_discrete_basic(distname, arg, first_case):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    np.random.seed(9765456)
+    rvs = distfn.rvs(size=2000, *arg)
+    supp = np.unique(rvs)
+    m, v = distfn.stats(*arg)
+    check_cdf_ppf(distfn, arg, supp, distname + ' cdf_ppf')
+
+    check_pmf_cdf(distfn, arg, distname)
+    check_oth(distfn, arg, supp, distname + ' oth')
+    check_edge_support(distfn, arg)
+
+    alpha = 0.01
+    check_discrete_chisquare(distfn, arg, rvs, alpha,
+           distname + ' chisquare')
+
+    if first_case:
+        locscale_defaults = (0,)
+        meths = [distfn.pmf, distfn.logpmf, distfn.cdf, distfn.logcdf,
+                 distfn.logsf]
+        # make sure arguments are within support
+        # for some distributions, this needs to be overridden
+        spec_k = {'randint': 11, 'hypergeom': 4, 'bernoulli': 0,
+                  'nchypergeom_wallenius': 6}
+        k = spec_k.get(distname, 1)
+        check_named_args(distfn, k, arg, locscale_defaults, meths)
+        if distname != 'sample distribution':
+            check_scale_docstring(distfn)
+        check_random_state_property(distfn, arg)
+        check_pickling(distfn, arg)
+        check_freezing(distfn, arg)
+
+        # Entropy
+        check_entropy(distfn, arg, distname)
+        if distfn.__class__._entropy != stats.rv_discrete._entropy:
+            check_private_entropy(distfn, arg, stats.rv_discrete)
+
+
+@pytest.mark.parametrize('distname,arg', distdiscrete)
+def test_moments(distname, arg):
+    try:
+        distfn = getattr(stats, distname)
+    except TypeError:
+        distfn = distname
+        distname = 'sample distribution'
+    m, v, s, k = distfn.stats(*arg, moments='mvsk')
+    check_normalization(distfn, arg, distname)
+
+    # compare `stats` and `moment` methods
+    check_moment(distfn, arg, m, v, distname)
+    check_mean_expect(distfn, arg, m, distname)
+    check_var_expect(distfn, arg, m, v, distname)
+    check_skew_expect(distfn, arg, m, v, s, distname)
+    if distname not in ['zipf', 'yulesimon']:
+        check_kurt_expect(distfn, arg, m, v, k, distname)
+
+    # frozen distr moments
+    check_moment_frozen(distfn, arg, m, 1)
+    check_moment_frozen(distfn, arg, v+m*m, 2)
+
+
+@pytest.mark.parametrize('dist,shape_args', distdiscrete)
+def test_rvs_broadcast(dist, shape_args):
+    # If shape_only is True, it means the _rvs method of the
+    # distribution uses more than one random number to generate a random
+    # variate.  That means the result of using rvs with broadcasting or
+    # with a nontrivial size will not necessarily be the same as using the
+    # numpy.vectorize'd version of rvs(), so we can only compare the shapes
+    # of the results, not the values.
+    # Whether or not a distribution is in the following list is an
+    # implementation detail of the distribution, not a requirement.  If
+    # the implementation the rvs() method of a distribution changes, this
+    # test might also have to be changed.
+    shape_only = dist in ['betabinom', 'skellam', 'yulesimon', 'dlaplace',
+                          'nchypergeom_fisher', 'nchypergeom_wallenius']
+
+    try:
+        distfunc = getattr(stats, dist)
+    except TypeError:
+        distfunc = dist
+        dist = 'rv_discrete(values=(%r, %r))' % (dist.xk, dist.pk)
+    loc = np.zeros(2)
+    nargs = distfunc.numargs
+    allargs = []
+    bshape = []
+    # Generate shape parameter arguments...
+    for k in range(nargs):
+        shp = (k + 3,) + (1,)*(k + 1)
+        param_val = shape_args[k]
+        allargs.append(np.full(shp, param_val))
+        bshape.insert(0, shp[0])
+    allargs.append(loc)
+    bshape.append(loc.size)
+    # bshape holds the expected shape when loc, scale, and the shape
+    # parameters are all broadcast together.
+    check_rvs_broadcast(distfunc, dist, allargs, bshape, shape_only, [np.int_])
+
+
+@pytest.mark.parametrize('dist,args', distdiscrete)
+def test_ppf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    #check with a negative, no and positive relocation.
+    np.random.seed(1942349)
+    re_locs = [np.random.randint(-10, -1), 0, np.random.randint(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        npt.assert_array_equal(
+            [_a-1+loc, _b+loc],
+            [distfn.ppf(0.0, *args, loc=loc), distfn.ppf(1.0, *args, loc=loc)]
+            )
+
+
+@pytest.mark.parametrize('dist, args', distdiscrete)
+def test_isf_with_loc(dist, args):
+    try:
+        distfn = getattr(stats, dist)
+    except TypeError:
+        distfn = dist
+    # check with a negative, no and positive relocation.
+    np.random.seed(1942349)
+    re_locs = [np.random.randint(-10, -1), 0, np.random.randint(1, 10)]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+    # test broadcasting behaviour
+    re_locs = [np.random.randint(-10, -1, size=(5, 3)),
+               np.zeros((5, 3)),
+               np.random.randint(1, 10, size=(5, 3))]
+    _a, _b = distfn.support(*args)
+    for loc in re_locs:
+        expected = _b + loc, _a - 1 + loc
+        res = distfn.isf(0., *args, loc=loc), distfn.isf(1., *args, loc=loc)
+        npt.assert_array_equal(expected, res)
+
+
+def check_cdf_ppf(distfn, arg, supp, msg):
+    # cdf is a step function, and ppf(q) = min{k : cdf(k) >= q, k integer}
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg), *arg),
+                           supp, msg + '-roundtrip')
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg) - 1e-8, *arg),
+                           supp, msg + '-roundtrip')
+
+    if not hasattr(distfn, 'xk'):
+        _a, _b = distfn.support(*arg)
+        supp1 = supp[supp < _b]
+        npt.assert_array_equal(distfn.ppf(distfn.cdf(supp1, *arg) + 1e-8, *arg),
+                               supp1 + distfn.inc, msg + ' ppf-cdf-next')
+        # -1e-8 could cause an error if pmf < 1e-8
+
+
+def check_pmf_cdf(distfn, arg, distname):
+    if hasattr(distfn, 'xk'):
+        index = distfn.xk
+    else:
+        startind = int(distfn.ppf(0.01, *arg) - 1)
+        index = list(range(startind, startind + 10))
+    cdfs = distfn.cdf(index, *arg)
+    pmfs_cum = distfn.pmf(index, *arg).cumsum()
+
+    atol, rtol = 1e-10, 1e-10
+    if distname == 'skellam':    # ncx2 accuracy
+        atol, rtol = 1e-5, 1e-5
+    npt.assert_allclose(cdfs - cdfs[0], pmfs_cum - pmfs_cum[0],
+                        atol=atol, rtol=rtol)
+
+
+def check_moment_frozen(distfn, arg, m, k):
+    npt.assert_allclose(distfn(*arg).moment(k), m,
+                        atol=1e-10, rtol=1e-10)
+
+
+def check_oth(distfn, arg, supp, msg):
+    # checking other methods of distfn
+    npt.assert_allclose(distfn.sf(supp, *arg), 1. - distfn.cdf(supp, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    q = np.linspace(0.01, 0.99, 20)
+    npt.assert_allclose(distfn.isf(q, *arg), distfn.ppf(1. - q, *arg),
+                        atol=1e-10, rtol=1e-10)
+
+    median_sf = distfn.isf(0.5, *arg)
+    npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
+    npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
+
+
+def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
+    """Perform chisquare test for random sample of a discrete distribution
+
+    Parameters
+    ----------
+    distname : string
+        name of distribution function
+    arg : sequence
+        parameters of distribution
+    alpha : float
+        significance level, threshold for p-value
+
+    Returns
+    -------
+    result : bool
+        0 if test passes, 1 if test fails
+
+    """
+    wsupp = 0.05
+
+    # construct intervals with minimum mass `wsupp`.
+    # intervals are left-half-open as in a cdf difference
+    _a, _b = distfn.support(*arg)
+    lo = int(max(_a, -1000))
+    high = int(min(_b, 1000)) + 1
+    distsupport = range(lo, high)
+    last = 0
+    distsupp = [lo]
+    distmass = []
+    for ii in distsupport:
+        current = distfn.cdf(ii, *arg)
+        if current - last >= wsupp - 1e-14:
+            distsupp.append(ii)
+            distmass.append(current - last)
+            last = current
+            if current > (1 - wsupp):
+                break
+    if distsupp[-1] < _b:
+        distsupp.append(_b)
+        distmass.append(1 - last)
+    distsupp = np.array(distsupp)
+    distmass = np.array(distmass)
+
+    # convert intervals to right-half-open as required by histogram
+    histsupp = distsupp + 1e-8
+    histsupp[0] = _a
+
+    # find sample frequencies and perform chisquare test
+    freq, hsupp = np.histogram(rvs, histsupp)
+    chis, pval = stats.chisquare(np.array(freq), len(rvs)*distmass)
+
+    npt.assert_(pval > alpha,
+                'chisquare - test for %s at arg = %s with pval = %s' %
+                (msg, str(arg), str(pval)))
+
+
+def check_scale_docstring(distfn):
+    if distfn.__doc__ is not None:
+        # Docstrings can be stripped if interpreter is run with -OO
+        npt.assert_('scale' not in distfn.__doc__)
+
+
+@pytest.mark.parametrize('method', ['pmf', 'logpmf', 'cdf', 'logcdf',
+                                    'sf', 'logsf', 'ppf', 'isf'])
+@pytest.mark.parametrize('distname, args', distdiscrete)
+def test_methods_with_lists(method, distname, args):
+    # Test that the discrete distributions can accept Python lists
+    # as arguments.
+    try:
+        dist = getattr(stats, distname)
+    except TypeError:
+        return
+    if method in ['ppf', 'isf']:
+        z = [0.1, 0.2]
+    else:
+        z = [0, 1]
+    p2 = [[p]*2 for p in args]
+    loc = [0, 1]
+    result = dist.pmf(z, *p2, loc=loc)
+    npt.assert_allclose(result,
+                        [dist.pmf(*v) for v in zip(z, *p2, loc)],
+                        rtol=1e-15, atol=1e-15)
+
+
+@pytest.mark.parametrize('distname, args', invdistdiscrete)
+def test_cdf_gh13280_regression(distname, args):
+    # Test for nan output when shape parameters are invalid
+    dist = getattr(stats, distname)
+    x = np.arange(-2, 15)
+    vals = dist.cdf(x, *args)
+    expected = np.nan
+    npt.assert_equal(vals, expected)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_discrete_distns.py

@@ -0,0 +1,546 @@
+import pytest
+from scipy.stats import (betabinom, hypergeom, nhypergeom, bernoulli,
+                         boltzmann, skellam, zipf, zipfian, binom, nbinom,
+                         nchypergeom_fisher, nchypergeom_wallenius, randint)
+
+import numpy as np
+from numpy.testing import (
+    assert_almost_equal, assert_equal, assert_allclose, suppress_warnings
+)
+from scipy.special import binom as special_binom
+from scipy.optimize import root_scalar
+from scipy.integrate import quad
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression CDF[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(3, 10, 4, 5,
+                           0.9761904761904762, 1e-15),
+                          (107, 10000, 3000, 215,
+                           0.9999999997226765, 1e-15),
+                          (10, 10000, 3000, 215,
+                           2.681682217692179e-21, 5e-11)])
+def test_hypergeom_cdf(k, M, n, N, expected, rtol):
+    p = hypergeom.cdf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+# The expected values were computed with Wolfram Alpha, using
+# the expression SurvivalFunction[HypergeometricDistribution[N, n, M], k].
+@pytest.mark.parametrize('k, M, n, N, expected, rtol',
+                         [(25, 10000, 3000, 215,
+                           0.9999999999052958, 1e-15),
+                          (125, 10000, 3000, 215,
+                           1.4416781705752128e-18, 5e-11)])
+def test_hypergeom_sf(k, M, n, N, expected, rtol):
+    p = hypergeom.sf(k, M, n, N)
+    assert_allclose(p, expected, rtol=rtol)
+
+
+def test_hypergeom_logpmf():
+    # symmetries test
+    # f(k,N,K,n) = f(n-k,N,N-K,n) = f(K-k,N,K,N-n) = f(k,N,n,K)
+    k = 5
+    N = 50
+    K = 10
+    n = 5
+    logpmf1 = hypergeom.logpmf(k, N, K, n)
+    logpmf2 = hypergeom.logpmf(n - k, N, N - K, n)
+    logpmf3 = hypergeom.logpmf(K - k, N, K, N - n)
+    logpmf4 = hypergeom.logpmf(k, N, n, K)
+    assert_almost_equal(logpmf1, logpmf2, decimal=12)
+    assert_almost_equal(logpmf1, logpmf3, decimal=12)
+    assert_almost_equal(logpmf1, logpmf4, decimal=12)
+
+    # test related distribution
+    # Bernoulli distribution if n = 1
+    k = 1
+    N = 10
+    K = 7
+    n = 1
+    hypergeom_logpmf = hypergeom.logpmf(k, N, K, n)
+    bernoulli_logpmf = bernoulli.logpmf(k, K/N)
+    assert_almost_equal(hypergeom_logpmf, bernoulli_logpmf, decimal=12)
+
+
+def test_nhypergeom_pmf():
+    # test with hypergeom
+    M, n, r = 45, 13, 8
+    k = 6
+    NHG = nhypergeom.pmf(k, M, n, r)
+    HG = hypergeom.pmf(k, M, n, k+r-1) * (M - n - (r-1)) / (M - (k+r-1))
+    assert_allclose(HG, NHG, rtol=1e-10)
+
+
+def test_nhypergeom_pmfcdf():
+    # test pmf and cdf with arbitrary values.
+    M = 8
+    n = 3
+    r = 4
+    support = np.arange(n+1)
+    pmf = nhypergeom.pmf(support, M, n, r)
+    cdf = nhypergeom.cdf(support, M, n, r)
+    assert_allclose(pmf, [1/14, 3/14, 5/14, 5/14], rtol=1e-13)
+    assert_allclose(cdf, [1/14, 4/14, 9/14, 1.0], rtol=1e-13)
+
+
+def test_nhypergeom_r0():
+    # test with `r = 0`.
+    M = 10
+    n = 3
+    r = 0
+    pmf = nhypergeom.pmf([[0, 1, 2, 0], [1, 2, 0, 3]], M, n, r)
+    assert_allclose(pmf, [[1, 0, 0, 1], [0, 0, 1, 0]], rtol=1e-13)
+
+
+def test_nhypergeom_rvs_shape():
+    # Check that when given a size with more dimensions than the
+    # dimensions of the broadcast parameters, rvs returns an array
+    # with the correct shape.
+    x = nhypergeom.rvs(22, [7, 8, 9], [[12], [13]], size=(5, 1, 2, 3))
+    assert x.shape == (5, 1, 2, 3)
+
+
+def test_nhypergeom_accuracy():
+    # Check that nhypergeom.rvs post-gh-13431 gives the same values as
+    # inverse transform sampling
+    np.random.seed(0)
+    x = nhypergeom.rvs(22, 7, 11, size=100)
+    np.random.seed(0)
+    p = np.random.uniform(size=100)
+    y = nhypergeom.ppf(p, 22, 7, 11)
+    assert_equal(x, y)
+
+
+def test_boltzmann_upper_bound():
+    k = np.arange(-3, 5)
+
+    N = 1
+    p = boltzmann.pmf(k, 0.123, N)
+    expected = k == 0
+    assert_equal(p, expected)
+
+    lam = np.log(2)
+    N = 3
+    p = boltzmann.pmf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 2/7, 1/7, 0, 0]
+    assert_allclose(p, expected, rtol=1e-13)
+
+    c = boltzmann.cdf(k, lam, N)
+    expected = [0, 0, 0, 4/7, 6/7, 1, 1, 1]
+    assert_allclose(c, expected, rtol=1e-13)
+
+
+def test_betabinom_a_and_b_unity():
+    # test limiting case that betabinom(n, 1, 1) is a discrete uniform
+    # distribution from 0 to n
+    n = 20
+    k = np.arange(n + 1)
+    p = betabinom(n, 1, 1).pmf(k)
+    expected = np.repeat(1 / (n + 1), n + 1)
+    assert_almost_equal(p, expected)
+
+
+def test_betabinom_bernoulli():
+    # test limiting case that betabinom(1, a, b) = bernoulli(a / (a + b))
+    a = 2.3
+    b = 0.63
+    k = np.arange(2)
+    p = betabinom(1, a, b).pmf(k)
+    expected = bernoulli(a / (a + b)).pmf(k)
+    assert_almost_equal(p, expected)
+
+
+def test_issue_10317():
+    alpha, n, p = 0.9, 10, 1
+    assert_equal(nbinom.interval(alpha=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_11134():
+    alpha, n, p = 0.95, 10, 0
+    assert_equal(binom.interval(alpha=alpha, n=n, p=p), (0, 0))
+
+
+def test_issue_7406():
+    np.random.seed(0)
+    assert_equal(binom.ppf(np.random.rand(10), 0, 0.5), 0)
+
+    # Also check that endpoints (q=0, q=1) are correct
+    assert_equal(binom.ppf(0, 0, 0.5), -1)
+    assert_equal(binom.ppf(1, 0, 0.5), 0)
+
+
+def test_issue_5122():
+    p = 0
+    n = np.random.randint(100, size=10)
+
+    x = 0
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, -1)
+
+    x = np.linspace(0.01, 0.99, 10)
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, 0)
+
+    x = 1
+    ppf = binom.ppf(x, n, p)
+    assert_equal(ppf, n)
+
+
+def test_issue_1603():
+    assert_equal(binom(1000, np.logspace(-3, -100)).ppf(0.01), 0)
+
+
+def test_issue_5503():
+    p = 0.5
+    x = np.logspace(3, 14, 12)
+    assert_allclose(binom.cdf(x, 2*x, p), 0.5, atol=1e-2)
+
+
+@pytest.mark.parametrize('x, n, p, cdf_desired', [
+    (300, 1000, 3/10, 0.51559351981411995636),
+    (3000, 10000, 3/10, 0.50493298381929698016),
+    (30000, 100000, 3/10, 0.50156000591726422864),
+    (300000, 1000000, 3/10, 0.50049331906666960038),
+    (3000000, 10000000, 3/10, 0.50015600124585261196),
+    (30000000, 100000000, 3/10, 0.50004933192735230102),
+    (30010000, 100000000, 3/10, 0.98545384016570790717),
+    (29990000, 100000000, 3/10, 0.01455017177985268670),
+    (29950000, 100000000, 3/10, 5.02250963487432024943e-28),
+])
+def test_issue_5503pt2(x, n, p, cdf_desired):
+    assert_allclose(binom.cdf(x, n, p), cdf_desired)
+
+
+def test_issue_5503pt3():
+    # From Wolfram Alpha: CDF[BinomialDistribution[1e12, 1e-12], 2]
+    assert_allclose(binom.cdf(2, 10**12, 10**-12), 0.91969860292869777384)
+
+
+def test_issue_6682():
+    # Reference value from R:
+    # options(digits=16)
+    # print(pnbinom(250, 50, 32/63, lower.tail=FALSE))
+    assert_allclose(nbinom.sf(250, 50, 32./63.), 1.460458510976452e-35)
+
+
+def test_skellam_gh11474():
+    # test issue reported in gh-11474 caused by `cdfchn`
+    mu = [1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000]
+    cdf = skellam.cdf(0, mu, mu)
+    # generated in R
+    # library(skellam)
+    # options(digits = 16)
+    # mu = c(1, 10, 100, 1000, 5000, 5050, 5100, 5250, 6000)
+    # pskellam(0, mu, mu, TRUE)
+    cdf_expected = [0.6542541612768356, 0.5448901559424127, 0.5141135799745580,
+                    0.5044605891382528, 0.5019947363350450, 0.5019848365953181,
+                    0.5019750827993392, 0.5019466621805060, 0.5018209330219539]
+    assert_allclose(cdf, cdf_expected)
+
+
+class TestZipfian:
+    def test_zipfian_asymptotic(self):
+        # test limiting case that zipfian(a, n) -> zipf(a) as n-> oo
+        a = 6.5
+        N = 10000000
+        k = np.arange(1, 21)
+        assert_allclose(zipfian.pmf(k, a, N), zipf.pmf(k, a))
+        assert_allclose(zipfian.cdf(k, a, N), zipf.cdf(k, a))
+        assert_allclose(zipfian.sf(k, a, N), zipf.sf(k, a))
+        assert_allclose(zipfian.stats(a, N, moments='msvk'),
+                        zipf.stats(a, moments='msvk'))
+
+    def test_zipfian_continuity(self):
+        # test that zipfian(0.999999, n) ~ zipfian(1.000001, n)
+        # (a = 1 switches between methods of calculating harmonic sum)
+        alt1, agt1 = 0.99999999, 1.00000001
+        N = 30
+        k = np.arange(1, N + 1)
+        assert_allclose(zipfian.pmf(k, alt1, N), zipfian.pmf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.cdf(k, alt1, N), zipfian.cdf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.sf(k, alt1, N), zipfian.sf(k, agt1, N),
+                        rtol=5e-7)
+        assert_allclose(zipfian.stats(alt1, N, moments='msvk'),
+                        zipfian.stats(agt1, N, moments='msvk'), rtol=5e-7)
+
+    def test_zipfian_R(self):
+        # test against R VGAM package
+        # library(VGAM)
+        # k <- c(13, 16,  1,  4,  4,  8, 10, 19,  5,  7)
+        # a <- c(1.56712977, 3.72656295, 5.77665117, 9.12168729, 5.79977172,
+        #        4.92784796, 9.36078764, 4.3739616 , 7.48171872, 4.6824154)
+        # n <- c(70, 80, 48, 65, 83, 89, 50, 30, 20, 20)
+        # pmf <- dzipf(k, N = n, shape = a)
+        # cdf <- pzipf(k, N = n, shape = a)
+        # print(pmf)
+        # print(cdf)
+        np.random.seed(0)
+        k = np.random.randint(1, 20, size=10)
+        a = np.random.rand(10)*10 + 1
+        n = np.random.randint(1, 100, size=10)
+        pmf = [8.076972e-03, 2.950214e-05, 9.799333e-01, 3.216601e-06,
+               3.158895e-04, 3.412497e-05, 4.350472e-10, 2.405773e-06,
+               5.860662e-06, 1.053948e-04]
+        cdf = [0.8964133, 0.9998666, 0.9799333, 0.9999995, 0.9998584,
+               0.9999458, 1.0000000, 0.9999920, 0.9999977, 0.9998498]
+        # skip the first point; zipUC is not accurate for low a, n
+        assert_allclose(zipfian.pmf(k, a, n)[1:], pmf[1:], rtol=1e-6)
+        assert_allclose(zipfian.cdf(k, a, n)[1:], cdf[1:], rtol=5e-5)
+
+    np.random.seed(0)
+    naive_tests = np.vstack((np.logspace(-2, 1, 10),
+                             np.random.randint(2, 40, 10))).T
+
+    @pytest.mark.parametrize("a, n", naive_tests)
+    def test_zipfian_naive(self, a, n):
+        # test against bare-bones implementation
+
+        @np.vectorize
+        def Hns(n, s):
+            """Naive implementation of harmonic sum"""
+            return (1/np.arange(1, n+1)**s).sum()
+
+        @np.vectorize
+        def pzip(k, a, n):
+            """Naive implementation of zipfian pmf"""
+            if k < 1 or k > n:
+                return 0.
+            else:
+                return 1 / k**a / Hns(n, a)
+
+        k = np.arange(n+1)
+        pmf = pzip(k, a, n)
+        cdf = np.cumsum(pmf)
+        mean = np.average(k, weights=pmf)
+        var = np.average((k - mean)**2, weights=pmf)
+        std = var**0.5
+        skew = np.average(((k-mean)/std)**3, weights=pmf)
+        kurtosis = np.average(((k-mean)/std)**4, weights=pmf) - 3
+        assert_allclose(zipfian.pmf(k, a, n), pmf)
+        assert_allclose(zipfian.cdf(k, a, n), cdf)
+        assert_allclose(zipfian.stats(a, n, moments="mvsk"),
+                        [mean, var, skew, kurtosis])
+
+
+class TestNCH():
+    np.random.seed(2)  # seeds 0 and 1 had some xl = xu; randint failed
+    shape = (2, 4, 3)
+    max_m = 100
+    m1 = np.random.randint(1, max_m, size=shape)    # red balls
+    m2 = np.random.randint(1, max_m, size=shape)    # white balls
+    N = m1 + m2                                     # total balls
+    n = randint.rvs(0, N, size=N.shape)             # number of draws
+    xl = np.maximum(0, n-m2)                        # lower bound of support
+    xu = np.minimum(n, m1)                          # upper bound of support
+    x = randint.rvs(xl, xu, size=xl.shape)
+    odds = np.random.rand(*x.shape)*2
+
+    # test output is more readable when function names (strings) are passed
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_nch_hypergeom(self, dist_name):
+        # Both noncentral hypergeometric distributions reduce to the
+        # hypergeometric distribution when odds = 1
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x, N, m1, n = self.x, self.N, self.m1, self.n
+        assert_allclose(dist.pmf(x, N, m1, n, odds=1),
+                        hypergeom.pmf(x, N, m1, n))
+
+    def test_nchypergeom_fisher_naive(self):
+        # test against a very simple implementation
+        x, N, m1, n, odds = self.x, self.N, self.m1, self.n, self.odds
+
+        @np.vectorize
+        def pmf_mean_var(x, N, m1, n, w):
+            # simple implementation of nchypergeom_fisher pmf
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                return t1 * t2 * w**x
+
+            def P(k):
+                return sum((f(y)*y**k for y in range(xl, xu + 1)))
+
+            P0 = P(0)
+            P1 = P(1)
+            P2 = P(2)
+            pmf = f(x) / P0
+            mean = P1 / P0
+            var = P2 / P0 - (P1 / P0)**2
+            return pmf, mean, var
+
+        pmf, mean, var = pmf_mean_var(x, N, m1, n, odds)
+        assert_allclose(nchypergeom_fisher.pmf(x, N, m1, n, odds), pmf)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='m'),
+                        mean)
+        assert_allclose(nchypergeom_fisher.stats(N, m1, n, odds, moments='v'),
+                        var)
+
+    def test_nchypergeom_wallenius_naive(self):
+        # test against a very simple implementation
+
+        np.random.seed(2)
+        shape = (2, 4, 3)
+        max_m = 100
+        m1 = np.random.randint(1, max_m, size=shape)
+        m2 = np.random.randint(1, max_m, size=shape)
+        N = m1 + m2
+        n = randint.rvs(0, N, size=N.shape)
+        xl = np.maximum(0, n-m2)
+        xu = np.minimum(n, m1)
+        x = randint.rvs(xl, xu, size=xl.shape)
+        w = np.random.rand(*x.shape)*2
+
+        def support(N, m1, n, w):
+            m2 = N - m1
+            xl = np.maximum(0, n-m2)
+            xu = np.minimum(n, m1)
+            return xl, xu
+
+        @np.vectorize
+        def mean(N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def fun(u):
+                return u/m1 + (1 - (n-u)/m2)**w - 1
+
+            return root_scalar(fun, bracket=(xl, xu)).root
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(nchypergeom_wallenius.mean(N, m1, n, w),
+                            mean(N, m1, n, w), rtol=2e-2)
+
+        @np.vectorize
+        def variance(N, m1, n, w):
+            m2 = N - m1
+            u = mean(N, m1, n, w)
+            a = u * (m1 - u)
+            b = (n-u)*(u + m2 - n)
+            return N*a*b / ((N-1) * (m1*b + m2*a))
+
+        with suppress_warnings() as sup:
+            sup.filter(RuntimeWarning,
+                       message="invalid value encountered in mean")
+            assert_allclose(
+                nchypergeom_wallenius.stats(N, m1, n, w, moments='v'),
+                variance(N, m1, n, w),
+                rtol=5e-2
+            )
+
+        @np.vectorize
+        def pmf(x, N, m1, n, w):
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+
+            def integrand(t):
+                D = w*(m1 - x) + (m2 - (n-x))
+                res = (1-t**(w/D))**x * (1-t**(1/D))**(n-x)
+                return res
+
+            def f(x):
+                t1 = special_binom(m1, x)
+                t2 = special_binom(m2, n - x)
+                the_integral = quad(integrand, 0, 1,
+                                    epsrel=1e-16, epsabs=1e-16)
+                return t1 * t2 * the_integral[0]
+
+            return f(x)
+
+        pmf0 = pmf(x, N, m1, n, w)
+        pmf1 = nchypergeom_wallenius.pmf(x, N, m1, n, w)
+
+        atol, rtol = 1e-6, 1e-6
+        i = np.abs(pmf1 - pmf0) < atol + rtol*np.abs(pmf0)
+        assert(i.sum() > np.prod(shape) / 2)  # works at least half the time
+
+        # for those that fail, discredit the naive implementation
+        for N, m1, n, w in zip(N[~i], m1[~i], n[~i], w[~i]):
+            # get the support
+            m2 = N - m1
+            xl, xu = support(N, m1, n, w)
+            x = np.arange(xl, xu + 1)
+
+            # calculate sum of pmf over the support
+            # the naive implementation is very wrong in these cases
+            assert pmf(x, N, m1, n, w).sum() < .5
+            assert_allclose(nchypergeom_wallenius.pmf(x, N, m1, n, w).sum(), 1)
+
+    def test_wallenius_against_mpmath(self):
+        # precompute data with mpmath since naive implementation above
+        # is not reliable. See source code in gh-13330.
+        M = 50
+        n = 30
+        N = 20
+        odds = 2.25
+        # Expected results, computed with mpmath.
+        sup = np.arange(21)
+        pmf = np.array([3.699003068656875e-20,
+                        5.89398584245431e-17,
+                        2.1594437742911123e-14,
+                        3.221458044649955e-12,
+                        2.4658279241205077e-10,
+                        1.0965862603981212e-08,
+                        3.057890479665704e-07,
+                        5.622818831643761e-06,
+                        7.056482841531681e-05,
+                        0.000618899425358671,
+                        0.003854172932571669,
+                        0.01720592676256026,
+                        0.05528844897093792,
+                        0.12772363313574242,
+                        0.21065898367825722,
+                        0.24465958845359234,
+                        0.1955114898110033,
+                        0.10355390084949237,
+                        0.03414490375225675,
+                        0.006231989845775931,
+                        0.0004715577304677075])
+        mean = 14.808018384813426
+        var = 2.6085975877923717
+
+        # nchypergeom_wallenius.pmf returns 0 for pmf(0) and pmf(1), and pmf(2)
+        # has only three digits of accuracy (~ 2.1511e-14).
+        assert_allclose(nchypergeom_wallenius.pmf(sup, M, n, N, odds), pmf,
+                        rtol=1e-13, atol=1e-13)
+        assert_allclose(nchypergeom_wallenius.mean(M, n, N, odds),
+                        mean, rtol=1e-13)
+        assert_allclose(nchypergeom_wallenius.var(M, n, N, odds),
+                        var, rtol=1e-11)
+
+    @pytest.mark.parametrize('dist_name',
+                             ['nchypergeom_fisher', 'nchypergeom_wallenius'])
+    def test_rvs_shape(self, dist_name):
+        # Check that when given a size with more dimensions than the
+        # dimensions of the broadcast parameters, rvs returns an array
+        # with the correct shape.
+        dists = {'nchypergeom_fisher': nchypergeom_fisher,
+                 'nchypergeom_wallenius': nchypergeom_wallenius}
+        dist = dists[dist_name]
+        x = dist.rvs(50, 30, [[10], [20]], [0.5, 1.0, 2.0], size=(5, 1, 2, 3))
+        assert x.shape == (5, 1, 2, 3)
+
+
+@pytest.mark.parametrize("mu, q, expected",
+                         [[10, 120, -1.240089881791596e-38],
+                          [1500, 0, -86.61466680572661]])
+def test_nbinom_11465(mu, q, expected):
+    # test nbinom.logcdf at extreme tails
+    size = 20
+    n, p = size, size/(size+mu)
+    # In R:
+    # options(digits=16)
+    # pnbinom(mu=10, size=20, q=120, log.p=TRUE)
+    assert_allclose(nbinom.logcdf(q, n, p), expected)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_entropy.py

@@ -0,0 +1,287 @@
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+# avoid new uses of the following; prefer assert/np.testing.assert_allclose
+from numpy.testing import (assert_, assert_almost_equal,
+                           assert_array_almost_equal)
+
+import pytest
+from pytest import raises as assert_raises
+import scipy.stats as stats
+
+
+class TestEntropy:
+    def test_entropy_positive(self):
+        # See ticket #497
+        pk = [0.5, 0.2, 0.3]
+        qk = [0.1, 0.25, 0.65]
+        eself = stats.entropy(pk, pk)
+        edouble = stats.entropy(pk, qk)
+        assert_(0.0 == eself)
+        assert_(edouble >= 0.0)
+
+    def test_entropy_base(self):
+        pk = np.ones(16, float)
+        S = stats.entropy(pk, base=2.)
+        assert_(abs(S - 4.) < 1.e-5)
+
+        qk = np.ones(16, float)
+        qk[:8] = 2.
+        S = stats.entropy(pk, qk)
+        S2 = stats.entropy(pk, qk, base=2.)
+        assert_(abs(S/S2 - np.log(2.)) < 1.e-5)
+
+    def test_entropy_zero(self):
+        # Test for PR-479
+        assert_almost_equal(stats.entropy([0, 1, 2]), 0.63651416829481278,
+                            decimal=12)
+
+    def test_entropy_2d(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
+        assert_array_almost_equal(stats.entropy(pk, qk),
+                                  [0.1933259, 0.18609809])
+
+    def test_entropy_2d_zero(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        qk = [[0.0, 0.1], [0.3, 0.6], [0.5, 0.3]]
+        assert_array_almost_equal(stats.entropy(pk, qk),
+                                  [np.inf, 0.18609809])
+
+        pk[0][0] = 0.0
+        assert_array_almost_equal(stats.entropy(pk, qk),
+                                  [0.17403988, 0.18609809])
+
+    def test_entropy_base_2d_nondefault_axis(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        assert_array_almost_equal(stats.entropy(pk, axis=1),
+                                  [0.63651417, 0.63651417, 0.66156324])
+
+    def test_entropy_2d_nondefault_axis(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
+        assert_array_almost_equal(stats.entropy(pk, qk, axis=1),
+                                  [0.231049, 0.231049, 0.127706])
+
+    def test_entropy_raises_value_error(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        qk = [[0.1, 0.2], [0.6, 0.3]]
+        assert_raises(ValueError, stats.entropy, pk, qk)
+
+    def test_base_entropy_with_axis_0_is_equal_to_default(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        assert_array_almost_equal(stats.entropy(pk, axis=0),
+                                  stats.entropy(pk))
+
+    def test_entropy_with_axis_0_is_equal_to_default(self):
+        pk = [[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]]
+        qk = [[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]]
+        assert_array_almost_equal(stats.entropy(pk, qk, axis=0),
+                                  stats.entropy(pk, qk))
+
+    def test_base_entropy_transposed(self):
+        pk = np.array([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        assert_array_almost_equal(stats.entropy(pk.T).T,
+                                  stats.entropy(pk, axis=1))
+
+    def test_entropy_transposed(self):
+        pk = np.array([[0.1, 0.2], [0.6, 0.3], [0.3, 0.5]])
+        qk = np.array([[0.2, 0.1], [0.3, 0.6], [0.5, 0.3]])
+        assert_array_almost_equal(stats.entropy(pk.T, qk.T).T,
+                                  stats.entropy(pk, qk, axis=1))
+
+    def test_entropy_broadcasting(self):
+        np.random.rand(0)
+        x = np.random.rand(3)
+        y = np.random.rand(2, 1)
+        res = stats.entropy(x, y, axis=-1)
+        assert_equal(res[0], stats.entropy(x, y[0]))
+        assert_equal(res[1], stats.entropy(x, y[1]))
+
+    def test_entropy_shape_mismatch(self):
+        x = np.random.rand(10, 1, 12)
+        y = np.random.rand(11, 2)
+        message = "shape mismatch: objects cannot be broadcast"
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, y)
+
+    def test_input_validation(self):
+        x = np.random.rand(10)
+        message = "`base` must be a positive number."
+        with pytest.raises(ValueError, match=message):
+            stats.entropy(x, base=-2)
+
+
+class TestDifferentialEntropy:
+    """
+    Vasicek results are compared with the R package vsgoftest.
+
+    # library(vsgoftest)
+    #
+    # samp <- c(<values>)
+    # entropy.estimate(x = samp, window = <window_length>)
+
+    """
+
+    def test_differential_entropy_vasicek(self):
+
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal(100)
+
+        entropy = stats.differential_entropy(values, method='vasicek')
+        assert_allclose(entropy, 1.342551, rtol=1e-6)
+
+        entropy = stats.differential_entropy(values, window_length=1,
+                                             method='vasicek')
+        assert_allclose(entropy, 1.122044, rtol=1e-6)
+
+        entropy = stats.differential_entropy(values, window_length=8,
+                                             method='vasicek')
+        assert_allclose(entropy, 1.349401, rtol=1e-6)
+
+    def test_differential_entropy_vasicek_2d_nondefault_axis(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+
+        entropy = stats.differential_entropy(values, axis=1, method='vasicek')
+        assert_allclose(
+            entropy,
+            [1.342551, 1.341826, 1.293775],
+            rtol=1e-6,
+        )
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=1,
+                                             method='vasicek')
+        assert_allclose(
+            entropy,
+            [1.122044, 1.102944, 1.129616],
+            rtol=1e-6,
+        )
+
+        entropy = stats.differential_entropy(values, axis=1, window_length=8,
+                                             method='vasicek')
+        assert_allclose(
+            entropy,
+            [1.349401, 1.338514, 1.292332],
+            rtol=1e-6,
+        )
+
+    def test_differential_entropy_raises_value_error(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+
+        error_str = (
+            r"Window length \({window_length}\) must be positive and less "
+            r"than half the sample size \({sample_size}\)."
+        )
+
+        sample_size = values.shape[1]
+
+        for window_length in {-1, 0, sample_size//2, sample_size}:
+
+            formatted_error_str = error_str.format(
+                window_length=window_length,
+                sample_size=sample_size,
+            )
+
+            with assert_raises(ValueError, match=formatted_error_str):
+                stats.differential_entropy(
+                    values,
+                    window_length=window_length,
+                    axis=1,
+                )
+
+    def test_base_differential_entropy_with_axis_0_is_equal_to_default(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((100, 3))
+
+        entropy = stats.differential_entropy(values, axis=0)
+        default_entropy = stats.differential_entropy(values)
+        assert_allclose(entropy, default_entropy)
+
+    def test_base_differential_entropy_transposed(self):
+        random_state = np.random.RandomState(0)
+        values = random_state.standard_normal((3, 100))
+
+        assert_allclose(
+            stats.differential_entropy(values.T).T,
+            stats.differential_entropy(values, axis=1),
+        )
+
+    def test_input_validation(self):
+        x = np.random.rand(10)
+
+        message = "`base` must be a positive number or `None`."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, base=-2)
+
+        message = "`method` must be one of..."
+        with pytest.raises(ValueError, match=message):
+            stats.differential_entropy(x, method='ekki-ekki')
+
+    @pytest.mark.parametrize('method', ['vasicek', 'van es',
+                                        'ebrahimi', 'correa'])
+    def test_consistency(self, method):
+        # test that method is a consistent estimator
+        n = 10000 if method == 'correa' else 1000000
+        rvs = stats.norm.rvs(size=n, random_state=0)
+        expected = stats.norm.entropy()
+        res = stats.differential_entropy(rvs, method=method)
+        assert_allclose(res, expected, rtol=0.005)
+
+    # values from differential_entropy reference [6], table 1, n=50, m=7
+    norm_rmse_std_cases = {  # method: (RMSE, STD)
+                           'vasicek': (0.198, 0.109),
+                           'van es': (0.212, 0.110),
+                           'correa': (0.135, 0.112),
+                           'ebrahimi': (0.128, 0.109)
+                           }
+
+    @pytest.mark.parametrize('method, expected',
+                             list(norm_rmse_std_cases.items()))
+    def test_norm_rmse_std(self, method, expected):
+        # test that RMSE and standard deviation of estimators matches values
+        # given in differential_entropy reference [6]. Incidentally, also
+        # tests vectorization.
+        reps, n, m = 10000, 50, 7
+        rmse_expected, std_expected = expected
+        rvs = stats.norm.rvs(size=(reps, n), random_state=0)
+        true_entropy = stats.norm.entropy()
+        res = stats.differential_entropy(rvs, window_length=m,
+                                         method=method, axis=-1)
+        assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
+                        rmse_expected, atol=0.005)
+        assert_allclose(np.std(res), std_expected, atol=0.002)
+
+    # values from differential_entropy reference [6], table 2, n=50, m=7
+    expon_rmse_std_cases = {  # method: (RMSE, STD)
+                            'vasicek': (0.194, 0.148),
+                            'van es': (0.179, 0.149),
+                            'correa': (0.155, 0.152),
+                            'ebrahimi': (0.151, 0.148)
+                            }
+
+    @pytest.mark.parametrize('method, expected',
+                             list(expon_rmse_std_cases.items()))
+    def test_expon_rmse_std(self, method, expected):
+        # test that RMSE and standard deviation of estimators matches values
+        # given in differential_entropy reference [6]. Incidentally, also
+        # tests vectorization.
+        reps, n, m = 10000, 50, 7
+        rmse_expected, std_expected = expected
+        rvs = stats.expon.rvs(size=(reps, n), random_state=0)
+        true_entropy = stats.expon.entropy()
+        res = stats.differential_entropy(rvs, window_length=m,
+                                         method=method, axis=-1)
+        assert_allclose(np.sqrt(np.mean((res - true_entropy)**2)),
+                        rmse_expected, atol=0.005)
+        assert_allclose(np.std(res), std_expected, atol=0.002)
+
+    @pytest.mark.parametrize('n, method', [(8, 'van es'),
+                                           (12, 'ebrahimi'),
+                                           (1001, 'vasicek')])
+    def test_method_auto(self, n, method):
+        rvs = stats.norm.rvs(size=(n,), random_state=0)
+        res1 = stats.differential_entropy(rvs)
+        res2 = stats.differential_entropy(rvs, method=method)
+        assert res1 == res2

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_fit.py

@@ -0,0 +1,141 @@
+import os
+
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+from scipy import stats
+
+from .test_continuous_basic import distcont
+
+# this is not a proper statistical test for convergence, but only
+# verifies that the estimate and true values don't differ by too much
+
+fit_sizes = [1000, 5000, 10000]  # sample sizes to try
+
+thresh_percent = 0.25  # percent of true parameters for fail cut-off
+thresh_min = 0.75  # minimum difference estimate - true to fail test
+
+mle_failing_fits = [
+        'burr',
+        'chi2',
+        'gausshyper',
+        'genexpon',
+        'gengamma',
+        'kappa4',
+        'ksone',
+        'kstwo',
+        'mielke',
+        'ncf',
+        'ncx2',
+        'pearson3',
+        'powerlognorm',
+        'truncexpon',
+        'tukeylambda',
+        'vonmises',
+        'levy_stable',
+        'trapezoid',
+        'studentized_range'
+]
+
+mm_failing_fits = ['alpha', 'betaprime', 'burr', 'burr12', 'cauchy', 'chi',
+                   'chi2', 'crystalball', 'dgamma', 'dweibull', 'f',
+                   'fatiguelife', 'fisk', 'foldcauchy', 'genextreme',
+                   'gengamma', 'genhyperbolic', 'gennorm', 'genpareto',
+                   'halfcauchy', 'invgamma', 'invweibull', 'johnsonsu',
+                   'kappa3', 'ksone', 'kstwo', 'levy', 'levy_l',
+                   'levy_stable', 'loglaplace', 'lomax', 'mielke', 'nakagami',
+                   'ncf', 'nct', 'ncx2', 'pareto', 'powerlognorm', 'powernorm',
+                   'skewcauchy', 't',
+                   'trapezoid', 'triang', 'tukeylambda', 'studentized_range']
+
+# not sure if these fail, but they caused my patience to fail
+mm_slow_fits = ['argus', 'exponpow', 'exponweib', 'gausshyper', 'genexpon',
+                'genhalflogistic', 'halfgennorm', 'gompertz', 'johnsonsb',
+                'kappa4', 'kstwobign', 'recipinvgauss', 'skewnorm',
+                'truncexpon', 'vonmises', 'vonmises_line']
+
+failing_fits = {"MM": mm_failing_fits + mm_slow_fits, "MLE": mle_failing_fits}
+
+# Don't run the fit test on these:
+skip_fit = [
+    'erlang',  # Subclass of gamma, generates a warning.
+]
+
+
+def cases_test_cont_fit():
+    # this tests the closeness of the estimated parameters to the true
+    # parameters with fit method of continuous distributions
+    # Note: is slow, some distributions don't converge with sample
+    # size <= 10000
+    for distname, arg in distcont:
+        if distname not in skip_fit:
+            yield distname, arg
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize('distname,arg', cases_test_cont_fit())
+@pytest.mark.parametrize('method', ["MLE", 'MM'])
+def test_cont_fit(distname, arg, method):
+    if distname in failing_fits[method]:
+        # Skip failing fits unless overridden
+        try:
+            xfail = not int(os.environ['SCIPY_XFAIL'])
+        except Exception:
+            xfail = True
+        if xfail:
+            msg = "Fitting %s doesn't work reliably yet" % distname
+            msg += (" [Set environment variable SCIPY_XFAIL=1 to run this"
+                    " test nevertheless.]")
+            pytest.xfail(msg)
+
+    distfn = getattr(stats, distname)
+
+    truearg = np.hstack([arg, [0.0, 1.0]])
+    diffthreshold = np.max(np.vstack([truearg*thresh_percent,
+                                      np.full(distfn.numargs+2, thresh_min)]),
+                           0)
+
+    for fit_size in fit_sizes:
+        # Note that if a fit succeeds, the other fit_sizes are skipped
+        np.random.seed(1234)
+
+        with np.errstate(all='ignore'):
+            rvs = distfn.rvs(size=fit_size, *arg)
+            est = distfn.fit(rvs, method=method)  # start with default values
+
+        diff = est - truearg
+
+        # threshold for location
+        diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,
+                                    thresh_min])
+
+        if np.any(np.isnan(est)):
+            raise AssertionError('nan returned in fit')
+        else:
+            if np.all(np.abs(diff) <= diffthreshold):
+                break
+    else:
+        txt = 'parameter: %s\n' % str(truearg)
+        txt += 'estimated: %s\n' % str(est)
+        txt += 'diff     : %s\n' % str(diff)
+        raise AssertionError('fit not very good in %s\n' % distfn.name + txt)
+
+
+def _check_loc_scale_mle_fit(name, data, desired, atol=None):
+    d = getattr(stats, name)
+    actual = d.fit(data)[-2:]
+    assert_allclose(actual, desired, atol=atol,
+                    err_msg='poor mle fit of (loc, scale) in %s' % name)
+
+
+def test_non_default_loc_scale_mle_fit():
+    data = np.array([1.01, 1.78, 1.78, 1.78, 1.88, 1.88, 1.88, 2.00])
+    _check_loc_scale_mle_fit('uniform', data, [1.01, 0.99], 1e-3)
+    _check_loc_scale_mle_fit('expon', data, [1.01, 0.73875], 1e-3)
+
+
+def test_expon_fit():
+    """gh-6167"""
+    data = [0, 0, 0, 0, 2, 2, 2, 2]
+    phat = stats.expon.fit(data, floc=0)
+    assert_allclose(phat, [0, 1.0], atol=1e-3)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_kdeoth.py

@@ -0,0 +1,488 @@
+from scipy import stats
+import numpy as np
+from numpy.testing import (assert_almost_equal, assert_,
+    assert_array_almost_equal, assert_array_almost_equal_nulp, assert_allclose)
+import pytest
+from pytest import raises as assert_raises
+
+
+def test_kde_1d():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+    xn = np.random.randn(n_basesample)
+    xnmean = xn.mean()
+    xnstd = xn.std(ddof=1)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate the density function for the kde for some points
+    xs = np.linspace(-7,7,501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+def test_kde_1d_weighted():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+    xn = np.random.randn(n_basesample)
+    wn = np.random.rand(n_basesample)
+    xnmean = np.average(xn, weights=wn)
+    xnstd = np.sqrt(np.average((xn-xnmean)**2, weights=wn))
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    # evaluate the density function for the kde for some points
+    xs = np.linspace(-7,7,501)
+    kdepdf = gkde.evaluate(xs)
+    normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
+    intervall = xs[1] - xs[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
+    prob1 = gkde.integrate_box_1d(xnmean, np.inf)
+    prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
+    assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
+
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*intervall, decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+@pytest.mark.slow
+def test_kde_2d():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn)
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]), mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large])
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]])
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+@pytest.mark.slow
+def test_kde_2d_weighted():
+    #some basic tests comparing to normal distribution
+    np.random.seed(8765678)
+    n_basesample = 500
+
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+
+    # Need transpose (shape (2, 500)) for kde
+    xn = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
+    wn = np.random.rand(n_basesample)
+
+    # get kde for original sample
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    # evaluate the density function for the kde for some points
+    x, y = np.mgrid[-7:7:500j, -7:7:500j]
+    grid_coords = np.vstack([x.ravel(), y.ravel()])
+    kdepdf = gkde.evaluate(grid_coords)
+    kdepdf = kdepdf.reshape(500, 500)
+
+    normpdf = stats.multivariate_normal.pdf(np.dstack([x, y]), mean=mean, cov=covariance)
+    intervall = y.ravel()[1] - y.ravel()[0]
+
+    assert_(np.sum((kdepdf - normpdf)**2) * (intervall**2) < 0.01)
+
+    small = -1e100
+    large = 1e100
+    prob1 = gkde.integrate_box([small, mean[1]], [large, large])
+    prob2 = gkde.integrate_box([small, small], [large, mean[1]])
+
+    assert_almost_equal(prob1, 0.5, decimal=1)
+    assert_almost_equal(prob2, 0.5, decimal=1)
+    assert_almost_equal(gkde.integrate_kde(gkde),
+                        (kdepdf**2).sum()*(intervall**2), decimal=2)
+    assert_almost_equal(gkde.integrate_gaussian(mean, covariance),
+                        (kdepdf*normpdf).sum()*(intervall**2), decimal=2)
+
+
+def test_kde_bandwidth_method():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.n, -1./(kde_obj.d+4))
+
+    np.random.seed(8765678)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+def test_kde_bandwidth_method_weighted():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.neff, -1./(kde_obj.d+4))
+
+    np.random.seed(8765678)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+# Subclasses that should stay working (extracted from various sources).
+# Unfortunately the earlier design of gaussian_kde made it necessary for users
+# to create these kinds of subclasses, or call _compute_covariance() directly.
+
+class _kde_subclass1(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.dataset = np.atleast_2d(dataset)
+        self.d, self.n = self.dataset.shape
+        self.covariance_factor = self.scotts_factor
+        self._compute_covariance()
+
+
+class _kde_subclass2(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.covariance_factor = self.scotts_factor
+        super().__init__(dataset)
+
+
+class _kde_subclass3(stats.gaussian_kde):
+    def __init__(self, dataset, covariance):
+        self.covariance = covariance
+        stats.gaussian_kde.__init__(self, dataset)
+
+    def _compute_covariance(self):
+        self.inv_cov = np.linalg.inv(self.covariance)
+        self._norm_factor = np.sqrt(np.linalg.det(2 * np.pi * self.covariance))
+
+
+class _kde_subclass4(stats.gaussian_kde):
+    def covariance_factor(self):
+        return 0.5 * self.silverman_factor()
+
+
+def test_gaussian_kde_subclassing():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # gaussian_kde itself
+    kde = stats.gaussian_kde(x1)
+    ys = kde(xs)
+
+    # subclass 1
+    kde1 = _kde_subclass1(x1)
+    y1 = kde1(xs)
+    assert_array_almost_equal_nulp(ys, y1, nulp=10)
+
+    # subclass 2
+    kde2 = _kde_subclass2(x1)
+    y2 = kde2(xs)
+    assert_array_almost_equal_nulp(ys, y2, nulp=10)
+
+    # subclass 3
+    kde3 = _kde_subclass3(x1, kde.covariance)
+    y3 = kde3(xs)
+    assert_array_almost_equal_nulp(ys, y3, nulp=10)
+
+    # subclass 4
+    kde4 = _kde_subclass4(x1)
+    y4 = kde4(x1)
+    y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
+
+    assert_array_almost_equal(y_expected, y4, decimal=6)
+
+    # Not a subclass, but check for use of _compute_covariance()
+    kde5 = kde
+    kde5.covariance_factor = lambda: kde.factor
+    kde5._compute_covariance()
+    y5 = kde5(xs)
+    assert_array_almost_equal_nulp(ys, y5, nulp=10)
+
+
+def test_gaussian_kde_covariance_caching():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=5)
+    # These expected values are from scipy 0.10, before some changes to
+    # gaussian_kde.  They were not compared with any external reference.
+    y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
+
+    # Set the bandwidth, then reset it to the default.
+    kde = stats.gaussian_kde(x1)
+    kde.set_bandwidth(bw_method=0.5)
+    kde.set_bandwidth(bw_method='scott')
+    y2 = kde(xs)
+
+    assert_array_almost_equal(y_expected, y2, decimal=7)
+
+
+def test_gaussian_kde_monkeypatch():
+    """Ugly, but people may rely on this.  See scipy pull request 123,
+    specifically the linked ML thread "Width of the Gaussian in stats.kde".
+    If it is necessary to break this later on, that is to be discussed on ML.
+    """
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # The old monkeypatched version to get at Silverman's Rule.
+    kde = stats.gaussian_kde(x1)
+    kde.covariance_factor = kde.silverman_factor
+    kde._compute_covariance()
+    y1 = kde(xs)
+
+    # The new saner version.
+    kde2 = stats.gaussian_kde(x1, bw_method='silverman')
+    y2 = kde2(xs)
+
+    assert_array_almost_equal_nulp(y1, y2, nulp=10)
+
+
+def test_kde_integer_input():
+    """Regression test for #1181."""
+    x1 = np.arange(5)
+    kde = stats.gaussian_kde(x1)
+    y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
+    assert_array_almost_equal(kde(x1), y_expected, decimal=6)
+
+
+_ftypes = ['float32', 'float64', 'float96', 'float128', 'int32', 'int64']
+
+@pytest.mark.parametrize("bw_type", _ftypes + ["scott", "silverman"])
+@pytest.mark.parametrize("weights_type", _ftypes)
+@pytest.mark.parametrize("dataset_type", _ftypes)
+@pytest.mark.parametrize("point_type", _ftypes)
+def test_kde_output_dtype(point_type, dataset_type, weights_type, bw_type):
+    # Check whether the datatypes are available
+    point_type = getattr(np, point_type, None)
+    dataset_type = getattr(np, weights_type, None)
+    weights_type = getattr(np, weights_type, None)
+
+    if bw_type in ["scott", "silverman"]:
+        bw = bw_type
+    else:
+        bw_type = getattr(np, bw_type, None)
+        bw = bw_type(3) if bw_type else None
+
+    if any(dt is None for dt in [point_type, dataset_type, weights_type, bw]):
+        pytest.skip()
+
+    weights = np.arange(5, dtype=weights_type)
+    dataset = np.arange(5, dtype=dataset_type)
+    k = stats.gaussian_kde(dataset, bw_method=bw, weights=weights)
+    points = np.arange(5, dtype=point_type)
+    result = k(points)
+    # weights are always cast to float64
+    assert result.dtype == np.result_type(dataset, points, np.float64(weights),
+                                          k.factor)
+
+
+def test_pdf_logpdf():
+    np.random.seed(1)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    gkde = stats.gaussian_kde(xs)
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+def test_pdf_logpdf_weighted():
+    np.random.seed(1)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+    wn = np.random.rand(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn, weights=wn)
+
+    xs = np.linspace(-15, 12, 25)
+    pdf = gkde.evaluate(xs)
+    pdf2 = gkde.pdf(xs)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+    logpdf = np.log(pdf)
+    logpdf2 = gkde.logpdf(xs)
+    assert_almost_equal(logpdf, logpdf2, decimal=12)
+
+    # There are more points than data
+    gkde = stats.gaussian_kde(xs, weights=np.random.rand(len(xs)))
+    pdf = np.log(gkde.evaluate(xn))
+    pdf2 = gkde.logpdf(xn)
+    assert_almost_equal(pdf, pdf2, decimal=12)
+
+
+@pytest.mark.xslow
+def test_logpdf_overflow():
+    # regression test for gh-12988; testing against linalg instability for
+    # very high dimensionality kde
+    np.random.seed(1)
+    n_dimensions = 2500
+    n_samples = 5000
+    xn = np.array([np.random.randn(n_samples) + (n) for n in range(
+        0, n_dimensions)])
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+
+    logpdf = gkde.logpdf(np.arange(0, n_dimensions))
+    np.testing.assert_equal(np.isneginf(logpdf[0]), False)
+    np.testing.assert_equal(np.isnan(logpdf[0]), False)
+
+
+def test_weights_intact():
+    # regression test for gh-9709: weights are not modified
+    np.random.seed(12345)
+    vals = np.random.lognormal(size=100)
+    weights = np.random.choice([1.0, 10.0, 100], size=vals.size)
+    orig_weights = weights.copy()
+
+    stats.gaussian_kde(np.log10(vals), weights=weights)
+    assert_allclose(weights, orig_weights, atol=1e-14, rtol=1e-14)
+
+
+def test_weights_integer():
+    # integer weights are OK, cf gh-9709 (comment)
+    np.random.seed(12345)
+    values = [0.2, 13.5, 21.0, 75.0, 99.0]
+    weights = [1, 2, 4, 8, 16]  # a list of integers
+    pdf_i = stats.gaussian_kde(values, weights=weights)
+    pdf_f = stats.gaussian_kde(values, weights=np.float64(weights))
+
+    xn = [0.3, 11, 88]
+    assert_allclose(pdf_i.evaluate(xn),
+                    pdf_f.evaluate(xn), atol=1e-14, rtol=1e-14)
+
+
+def test_seed():
+    # Test the seed option of the resample method
+    def test_seed_sub(gkde_trail):
+        n_sample = 200
+        # The results should be different without using seed
+        samp1 = gkde_trail.resample(n_sample)
+        samp2 = gkde_trail.resample(n_sample)
+        assert_raises(
+            AssertionError, assert_allclose, samp1, samp2, atol=1e-13
+        )
+        # Use integer seed
+        seed = 831
+        samp1 = gkde_trail.resample(n_sample, seed=seed)
+        samp2 = gkde_trail.resample(n_sample, seed=seed)
+        assert_allclose(samp1, samp2, atol=1e-13)
+        # Use RandomState
+        rstate1 = np.random.RandomState(seed=138)
+        samp1 = gkde_trail.resample(n_sample, seed=rstate1)
+        rstate2 = np.random.RandomState(seed=138)
+        samp2 = gkde_trail.resample(n_sample, seed=rstate2)
+        assert_allclose(samp1, samp2, atol=1e-13)
+
+        # check that np.random.Generator can be used (numpy >= 1.17)
+        if hasattr(np.random, 'default_rng'):
+            # obtain a np.random.Generator object
+            rng = np.random.default_rng(1234)
+            gkde_trail.resample(n_sample, seed=rng)
+
+    np.random.seed(8765678)
+    n_basesample = 500
+    wn = np.random.rand(n_basesample)
+    # Test 1D case
+    xn_1d = np.random.randn(n_basesample)
+
+    gkde_1d = stats.gaussian_kde(xn_1d)
+    test_seed_sub(gkde_1d)
+    gkde_1d_weighted = stats.gaussian_kde(xn_1d, weights=wn)
+    test_seed_sub(gkde_1d_weighted)
+
+    # Test 2D case
+    mean = np.array([1.0, 3.0])
+    covariance = np.array([[1.0, 2.0], [2.0, 6.0]])
+    xn_2d = np.random.multivariate_normal(mean, covariance, size=n_basesample).T
+
+    gkde_2d = stats.gaussian_kde(xn_2d)
+    test_seed_sub(gkde_2d)
+    gkde_2d_weighted = stats.gaussian_kde(xn_2d, weights=wn)
+    test_seed_sub(gkde_2d_weighted)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_mstats_extras.py

@@ -0,0 +1,134 @@
+import numpy as np
+import numpy.ma as ma
+import scipy.stats.mstats as ms
+
+from numpy.testing import (assert_equal, assert_almost_equal, assert_,
+    assert_allclose)
+
+
+def test_compare_medians_ms():
+    x = np.arange(7)
+    y = x + 10
+    assert_almost_equal(ms.compare_medians_ms(x, y), 0)
+
+    y2 = np.linspace(0, 1, num=10)
+    assert_almost_equal(ms.compare_medians_ms(x, y2), 0.017116406778)
+
+
+def test_hdmedian():
+    # 1-D array
+    x = ma.arange(11)
+    assert_allclose(ms.hdmedian(x), 5, rtol=1e-14)
+    x.mask = ma.make_mask(x)
+    x.mask[:7] = False
+    assert_allclose(ms.hdmedian(x), 3, rtol=1e-14)
+
+    # Check that `var` keyword returns a value.  TODO: check whether returned
+    # value is actually correct.
+    assert_(ms.hdmedian(x, var=True).size == 2)
+
+    # 2-D array
+    x2 = ma.arange(22).reshape((11, 2))
+    assert_allclose(ms.hdmedian(x2, axis=0), [10, 11])
+    x2.mask = ma.make_mask(x2)
+    x2.mask[:7, :] = False
+    assert_allclose(ms.hdmedian(x2, axis=0), [6, 7])
+
+
+def test_rsh():
+    np.random.seed(132345)
+    x = np.random.randn(100)
+    res = ms.rsh(x)
+    # Just a sanity check that the code runs and output shape is correct.
+    # TODO: check that implementation is correct.
+    assert_(res.shape == x.shape)
+
+    # Check points keyword
+    res = ms.rsh(x, points=[0, 1.])
+    assert_(res.size == 2)
+
+
+def test_mjci():
+    # Tests the Marits-Jarrett estimator
+    data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
+                      296,299,306,376,428,515,666,1310,2611])
+    assert_almost_equal(ms.mjci(data),[55.76819,45.84028,198.87875],5)
+
+
+def test_trimmed_mean_ci():
+    # Tests the confidence intervals of the trimmed mean.
+    data = ma.array([545,555,558,572,575,576,578,580,
+                     594,605,635,651,653,661,666])
+    assert_almost_equal(ms.trimmed_mean(data,0.2), 596.2, 1)
+    assert_equal(np.round(ms.trimmed_mean_ci(data,(0.2,0.2)),1),
+                 [561.8, 630.6])
+
+
+def test_idealfourths():
+    # Tests ideal-fourths
+    test = np.arange(100)
+    assert_almost_equal(np.asarray(ms.idealfourths(test)),
+                        [24.416667,74.583333],6)
+    test_2D = test.repeat(3).reshape(-1,3)
+    assert_almost_equal(ms.idealfourths(test_2D, axis=0),
+                        [[24.416667,24.416667,24.416667],
+                         [74.583333,74.583333,74.583333]],6)
+    assert_almost_equal(ms.idealfourths(test_2D, axis=1),
+                        test.repeat(2).reshape(-1,2))
+    test = [0, 0]
+    _result = ms.idealfourths(test)
+    assert_(np.isnan(_result).all())
+
+
+class TestQuantiles:
+    data = [0.706560797,0.727229578,0.990399276,0.927065621,0.158953014,
+        0.887764025,0.239407086,0.349638551,0.972791145,0.149789972,
+        0.936947700,0.132359948,0.046041972,0.641675031,0.945530547,
+        0.224218684,0.771450991,0.820257774,0.336458052,0.589113496,
+        0.509736129,0.696838829,0.491323573,0.622767425,0.775189248,
+        0.641461450,0.118455200,0.773029450,0.319280007,0.752229111,
+        0.047841438,0.466295911,0.583850781,0.840581845,0.550086491,
+        0.466470062,0.504765074,0.226855960,0.362641207,0.891620942,
+        0.127898691,0.490094097,0.044882048,0.041441695,0.317976349,
+        0.504135618,0.567353033,0.434617473,0.636243375,0.231803616,
+        0.230154113,0.160011327,0.819464108,0.854706985,0.438809221,
+        0.487427267,0.786907310,0.408367937,0.405534192,0.250444460,
+        0.995309248,0.144389588,0.739947527,0.953543606,0.680051621,
+        0.388382017,0.863530727,0.006514031,0.118007779,0.924024803,
+        0.384236354,0.893687694,0.626534881,0.473051932,0.750134705,
+        0.241843555,0.432947602,0.689538104,0.136934797,0.150206859,
+        0.474335206,0.907775349,0.525869295,0.189184225,0.854284286,
+        0.831089744,0.251637345,0.587038213,0.254475554,0.237781276,
+        0.827928620,0.480283781,0.594514455,0.213641488,0.024194386,
+        0.536668589,0.699497811,0.892804071,0.093835427,0.731107772]
+
+    def test_hdquantiles(self):
+        data = self.data
+        assert_almost_equal(ms.hdquantiles(data,[0., 1.]),
+                            [0.006514031, 0.995309248])
+        hdq = ms.hdquantiles(data,[0.25, 0.5, 0.75])
+        assert_almost_equal(hdq, [0.253210762, 0.512847491, 0.762232442,])
+        hdq = ms.hdquantiles_sd(data,[0.25, 0.5, 0.75])
+        assert_almost_equal(hdq, [0.03786954, 0.03805389, 0.03800152,], 4)
+
+        data = np.array(data).reshape(10,10)
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0)
+        assert_almost_equal(hdq[:,0], ms.hdquantiles(data[:,0],[0.25,0.5,0.75]))
+        assert_almost_equal(hdq[:,-1], ms.hdquantiles(data[:,-1],[0.25,0.5,0.75]))
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0,var=True)
+        assert_almost_equal(hdq[...,0],
+                            ms.hdquantiles(data[:,0],[0.25,0.5,0.75],var=True))
+        assert_almost_equal(hdq[...,-1],
+                            ms.hdquantiles(data[:,-1],[0.25,0.5,0.75], var=True))
+
+    def test_hdquantiles_sd(self):
+        # Only test that code runs, implementation not checked for correctness
+        res = ms.hdquantiles_sd(self.data)
+        assert_(res.size == 3)
+
+    def test_mquantiles_cimj(self):
+        # Only test that code runs, implementation not checked for correctness
+        ci_lower, ci_upper = ms.mquantiles_cimj(self.data)
+        assert_(ci_lower.size == ci_upper.size == 3)
+
+

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_rank.py

@@ -0,0 +1,241 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal
+
+from scipy.stats import rankdata, tiecorrect
+import pytest
+
+
+class TestTieCorrect:
+
+    def test_empty(self):
+        """An empty array requires no correction, should return 1.0."""
+        ranks = np.array([], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_one(self):
+        """A single element requires no correction, should return 1.0."""
+        ranks = np.array([1.0], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_no_correction(self):
+        """Arrays with no ties require no correction."""
+        ranks = np.arange(2.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+        ranks = np.arange(3.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_basic(self):
+        """Check a few basic examples of the tie correction factor."""
+        # One tie of two elements
+        ranks = np.array([1.0, 2.5, 2.5])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of two elements (same as above, but tie is not at the end)
+        ranks = np.array([1.5, 1.5, 3.0])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of three elements
+        ranks = np.array([1.0, 3.0, 3.0, 3.0])
+        c = tiecorrect(ranks)
+        T = 3.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # Two ties, lengths 2 and 3.
+        ranks = np.array([1.5, 1.5, 4.0, 4.0, 4.0])
+        c = tiecorrect(ranks)
+        T1 = 2.0
+        T2 = 3.0
+        N = ranks.size
+        expected = 1.0 - ((T1**3 - T1) + (T2**3 - T2)) / (N**3 - N)
+        assert_equal(c, expected)
+
+    def test_overflow(self):
+        ntie, k = 2000, 5
+        a = np.repeat(np.arange(k), ntie)
+        n = a.size  # ntie * k
+        out = tiecorrect(rankdata(a))
+        assert_equal(out, 1.0 - k * (ntie**3 - ntie) / float(n**3 - n))
+
+
+class TestRankData:
+
+    def test_empty(self):
+        """stats.rankdata([]) should return an empty array."""
+        a = np.array([], dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, np.array([], dtype=np.float64))
+        r = rankdata([])
+        assert_array_equal(r, np.array([], dtype=np.float64))
+
+    def test_one(self):
+        """Check stats.rankdata with an array of length 1."""
+        data = [100]
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, np.array([1.0], dtype=np.float64))
+        r = rankdata(data)
+        assert_array_equal(r, np.array([1.0], dtype=np.float64))
+
+    def test_basic(self):
+        """Basic tests of stats.rankdata."""
+        data = [100, 10, 50]
+        expected = np.array([3.0, 1.0, 2.0], dtype=np.float64)
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+
+        data = [40, 10, 30, 10, 50]
+        expected = np.array([4.0, 1.5, 3.0, 1.5, 5.0], dtype=np.float64)
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+
+        data = [20, 20, 20, 10, 10, 10]
+        expected = np.array([5.0, 5.0, 5.0, 2.0, 2.0, 2.0], dtype=np.float64)
+        a = np.array(data, dtype=int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+        # The docstring states explicitly that the argument is flattened.
+        a2d = a.reshape(2, 3)
+        r = rankdata(a2d)
+        assert_array_equal(r, expected)
+
+    def test_rankdata_object_string(self):
+        min_rank = lambda a: [1 + sum(i < j for i in a) for j in a]
+        max_rank = lambda a: [sum(i <= j for i in a) for j in a]
+        ordinal_rank = lambda a: min_rank([(x, i) for i, x in enumerate(a)])
+
+        def average_rank(a):
+            return [(i + j) / 2.0 for i, j in zip(min_rank(a), max_rank(a))]
+
+        def dense_rank(a):
+            b = np.unique(a)
+            return [1 + sum(i < j for i in b) for j in a]
+
+        rankf = dict(min=min_rank, max=max_rank, ordinal=ordinal_rank,
+                     average=average_rank, dense=dense_rank)
+
+        def check_ranks(a):
+            for method in 'min', 'max', 'dense', 'ordinal', 'average':
+                out = rankdata(a, method=method)
+                assert_array_equal(out, rankf[method](a))
+
+        val = ['foo', 'bar', 'qux', 'xyz', 'abc', 'efg', 'ace', 'qwe', 'qaz']
+        check_ranks(np.random.choice(val, 200))
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+        val = np.array([0, 1, 2, 2.718, 3, 3.141], dtype='object')
+        check_ranks(np.random.choice(val, 200).astype('object'))
+
+    def test_large_int(self):
+        data = np.array([2**60, 2**60+1], dtype=np.uint64)
+        r = rankdata(data)
+        assert_array_equal(r, [1.0, 2.0])
+
+        data = np.array([2**60, 2**60+1], dtype=np.int64)
+        r = rankdata(data)
+        assert_array_equal(r, [1.0, 2.0])
+
+        data = np.array([2**60, -2**60+1], dtype=np.int64)
+        r = rankdata(data)
+        assert_array_equal(r, [2.0, 1.0])
+
+    def test_big_tie(self):
+        for n in [10000, 100000, 1000000]:
+            data = np.ones(n, dtype=int)
+            r = rankdata(data)
+            expected_rank = 0.5 * (n + 1)
+            assert_array_equal(r, expected_rank * data,
+                               "test failed with n=%d" % n)
+
+    def test_axis(self):
+        data = [[0, 2, 1],
+                [4, 2, 2]]
+        expected0 = [[1., 1.5, 1.],
+                     [2., 1.5, 2.]]
+        r0 = rankdata(data, axis=0)
+        assert_array_equal(r0, expected0)
+        expected1 = [[1., 3., 2.],
+                     [3., 1.5, 1.5]]
+        r1 = rankdata(data, axis=1)
+        assert_array_equal(r1, expected1)
+
+    methods = ["average", "min", "max", "dense", "ordinal"]
+    dtypes = [np.float64] + [np.int_]*4
+
+    @pytest.mark.parametrize("axis", [0, 1])
+    @pytest.mark.parametrize("method, dtype", zip(methods, dtypes))
+    def test_size_0_axis(self, axis, method, dtype):
+        shape = (3, 0)
+        data = np.zeros(shape)
+        r = rankdata(data, method=method, axis=axis)
+        assert_equal(r.shape, shape)
+        assert_equal(r.dtype, dtype)
+
+
+_cases = (
+    # values, method, expected
+    ([], 'average', []),
+    ([], 'min', []),
+    ([], 'max', []),
+    ([], 'dense', []),
+    ([], 'ordinal', []),
+    #
+    ([100], 'average', [1.0]),
+    ([100], 'min', [1.0]),
+    ([100], 'max', [1.0]),
+    ([100], 'dense', [1.0]),
+    ([100], 'ordinal', [1.0]),
+    #
+    ([100, 100, 100], 'average', [2.0, 2.0, 2.0]),
+    ([100, 100, 100], 'min', [1.0, 1.0, 1.0]),
+    ([100, 100, 100], 'max', [3.0, 3.0, 3.0]),
+    ([100, 100, 100], 'dense', [1.0, 1.0, 1.0]),
+    ([100, 100, 100], 'ordinal', [1.0, 2.0, 3.0]),
+    #
+    ([100, 300, 200], 'average', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'min', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'max', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'dense', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'ordinal', [1.0, 3.0, 2.0]),
+    #
+    ([100, 200, 300, 200], 'average', [1.0, 2.5, 4.0, 2.5]),
+    ([100, 200, 300, 200], 'min', [1.0, 2.0, 4.0, 2.0]),
+    ([100, 200, 300, 200], 'max', [1.0, 3.0, 4.0, 3.0]),
+    ([100, 200, 300, 200], 'dense', [1.0, 2.0, 3.0, 2.0]),
+    ([100, 200, 300, 200], 'ordinal', [1.0, 2.0, 4.0, 3.0]),
+    #
+    ([100, 200, 300, 200, 100], 'average', [1.5, 3.5, 5.0, 3.5, 1.5]),
+    ([100, 200, 300, 200, 100], 'min', [1.0, 3.0, 5.0, 3.0, 1.0]),
+    ([100, 200, 300, 200, 100], 'max', [2.0, 4.0, 5.0, 4.0, 2.0]),
+    ([100, 200, 300, 200, 100], 'dense', [1.0, 2.0, 3.0, 2.0, 1.0]),
+    ([100, 200, 300, 200, 100], 'ordinal', [1.0, 3.0, 5.0, 4.0, 2.0]),
+    #
+    ([10] * 30, 'ordinal', np.arange(1.0, 31.0)),
+)
+
+
+def test_cases():
+    for values, method, expected in _cases:
+        r = rankdata(values, method=method)
+        assert_array_equal(r, expected)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_relative_risk.py

@@ -0,0 +1,96 @@
+
+import pytest
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from scipy.stats.contingency import relative_risk
+
+
+# Test just the calculation of the relative risk, including edge
+# cases that result in a relative risk of 0, inf or nan.
+@pytest.mark.parametrize(
+    'exposed_cases, exposed_total, control_cases, control_total, expected_rr',
+    [(1, 4, 3, 8, 0.25 / 0.375),
+     (0, 10, 5, 20, 0),
+     (0, 10, 0, 20, np.nan),
+     (5, 15, 0, 20, np.inf)]
+)
+def test_relative_risk(exposed_cases, exposed_total,
+                       control_cases, control_total, expected_rr):
+    result = relative_risk(exposed_cases, exposed_total,
+                           control_cases, control_total)
+    assert_allclose(result.relative_risk, expected_rr, rtol=1e-13)
+
+
+def test_relative_risk_confidence_interval():
+    result = relative_risk(exposed_cases=16, exposed_total=128,
+                           control_cases=24, control_total=256)
+    rr = result.relative_risk
+    ci = result.confidence_interval(confidence_level=0.95)
+    # The corresponding calculation in R using the epitools package.
+    #
+    # > library(epitools)
+    # > c <- matrix(c(232, 112, 24, 16), nrow=2)
+    # > result <- riskratio(c)
+    # > result$measure
+    #               risk ratio with 95% C.I.
+    # Predictor  estimate     lower    upper
+    #   Exposed1 1.000000        NA       NA
+    #   Exposed2 1.333333 0.7347317 2.419628
+    #
+    # The last line is the result that we want.
+    assert_allclose(rr, 4/3)
+    assert_allclose((ci.low, ci.high), (0.7347317, 2.419628), rtol=5e-7)
+
+
+def test_relative_risk_ci_conflevel0():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    rr = result.relative_risk
+    assert_allclose(rr, 2.0, rtol=1e-14)
+    ci = result.confidence_interval(0)
+    assert_allclose((ci.low, ci.high), (2.0, 2.0), rtol=1e-12)
+
+
+def test_relative_risk_ci_conflevel1():
+    result = relative_risk(exposed_cases=4, exposed_total=12,
+                           control_cases=5, control_total=30)
+    ci = result.confidence_interval(1)
+    assert_equal((ci.low, ci.high), (0, np.inf))
+
+
+def test_relative_risk_ci_edge_cases_00():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.nan)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_01():
+    result = relative_risk(exposed_cases=0, exposed_total=12,
+                           control_cases=1, control_total=30)
+    assert_equal(result.relative_risk, 0)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (0.0, np.nan))
+
+
+def test_relative_risk_ci_edge_cases_10():
+    result = relative_risk(exposed_cases=1, exposed_total=12,
+                           control_cases=0, control_total=30)
+    assert_equal(result.relative_risk, np.inf)
+    ci = result.confidence_interval()
+    assert_equal((ci.low, ci.high), (np.nan, np.inf))
+
+
+@pytest.mark.parametrize('ec, et, cc, ct', [(0, 0, 10, 20),
+                                            (-1, 10, 1, 5),
+                                            (1, 10, 0, 0),
+                                            (1, 10, -1, 4)])
+def test_relative_risk_bad_value(ec, et, cc, ct):
+    with pytest.raises(ValueError, match="must be an integer not less than"):
+        relative_risk(ec, et, cc, ct)
+
+
+def test_relative_risk_bad_type():
+    with pytest.raises(TypeError, match="must be an integer"):
+        relative_risk(1, 10, 2.0, 40)

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_tukeylambda_stats.py

@@ -0,0 +1,86 @@
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+
+from scipy.stats._tukeylambda_stats import (tukeylambda_variance,
+                                            tukeylambda_kurtosis)
+
+
+def test_tukeylambda_stats_known_exact():
+    """Compare results with some known exact formulas."""
+    # Some exact values of the Tukey Lambda variance and kurtosis:
+    # lambda   var      kurtosis
+    #   0     pi**2/3     6/5     (logistic distribution)
+    #  0.5    4 - pi    (5/3 - pi/2)/(pi/4 - 1)**2 - 3
+    #   1      1/3       -6/5     (uniform distribution on (-1,1))
+    #   2      1/12      -6/5     (uniform distribution on (-1/2, 1/2))
+
+    # lambda = 0
+    var = tukeylambda_variance(0)
+    assert_allclose(var, np.pi**2 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0)
+    assert_allclose(kurt, 1.2, atol=1e-10)
+
+    # lambda = 0.5
+    var = tukeylambda_variance(0.5)
+    assert_allclose(var, 4 - np.pi, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0.5)
+    desired = (5./3 - np.pi/2) / (np.pi/4 - 1)**2 - 3
+    assert_allclose(kurt, desired, atol=1e-10)
+
+    # lambda = 1
+    var = tukeylambda_variance(1)
+    assert_allclose(var, 1.0 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(1)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+    # lambda = 2
+    var = tukeylambda_variance(2)
+    assert_allclose(var, 1.0 / 12, atol=1e-12)
+    kurt = tukeylambda_kurtosis(2)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+
+def test_tukeylambda_stats_mpmath():
+    """Compare results with some values that were computed using mpmath."""
+    a10 = dict(atol=1e-10, rtol=0)
+    a12 = dict(atol=1e-12, rtol=0)
+    data = [
+        # lambda        variance              kurtosis
+        [-0.1, 4.78050217874253547, 3.78559520346454510],
+        [-0.0649, 4.16428023599895777, 2.52019675947435718],
+        [-0.05, 3.93672267890775277, 2.13129793057777277],
+        [-0.001, 3.30128380390964882, 1.21452460083542988],
+        [0.001, 3.27850775649572176, 1.18560634779287585],
+        [0.03125, 2.95927803254615800, 0.804487555161819980],
+        [0.05, 2.78281053405464501, 0.611604043886644327],
+        [0.0649, 2.65282386754100551, 0.476834119532774540],
+        [1.2, 0.242153920578588346, -1.23428047169049726],
+        [10.0, 0.00095237579757703597, 2.37810697355144933],
+        [20.0, 0.00012195121951131043, 7.37654321002709531],
+    ]
+
+    for lam, var_expected, kurt_expected in data:
+        var = tukeylambda_variance(lam)
+        assert_allclose(var, var_expected, **a12)
+        kurt = tukeylambda_kurtosis(lam)
+        assert_allclose(kurt, kurt_expected, **a10)
+
+    # Test with vector arguments (most of the other tests are for single
+    # values).
+    lam, var_expected, kurt_expected = zip(*data)
+    var = tukeylambda_variance(lam)
+    assert_allclose(var, var_expected, **a12)
+    kurt = tukeylambda_kurtosis(lam)
+    assert_allclose(kurt, kurt_expected, **a10)
+
+
+def test_tukeylambda_stats_invalid():
+    """Test values of lambda outside the domains of the functions."""
+    lam = [-1.0, -0.5]
+    var = tukeylambda_variance(lam)
+    assert_equal(var, np.array([np.nan, np.inf]))
+
+    lam = [-1.0, -0.25]
+    kurt = tukeylambda_kurtosis(lam)
+    assert_equal(kurt, np.array([np.nan, np.inf]))
+

dashboard/flask-server/venv/Lib/site-packages/scipy/stats/tests/test_variation.py

@@ -0,0 +1,158 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose
+import pytest
+from scipy.stats import variation
+
+
+class TestVariation:
+    """
+    Test class for scipy.stats.variation
+    """
+
+    def test_ddof(self):
+        x = np.arange(9.0)
+        assert_allclose(variation(x, ddof=1), np.sqrt(60/8)/4)
+
+    @pytest.mark.parametrize('sgn', [1, -1])
+    def test_sign(self, sgn):
+        x = np.array([1, 2, 3, 4, 5])
+        v = variation(sgn*x)
+        expected = sgn*np.sqrt(2)/3
+        assert_allclose(v, expected, rtol=1e-10)
+
+    def test_scalar(self):
+        # A scalar is treated like a 1-d sequence with length 1.
+        assert_equal(variation(4.0), 0.0)
+
+    @pytest.mark.parametrize('nan_policy, expected',
+                             [('propagate', np.nan),
+                              ('omit', np.sqrt(20/3)/4)])
+    def test_variation_nan(self, nan_policy, expected):
+        x = np.arange(10.)
+        x[9] = np.nan
+        assert_allclose(variation(x, nan_policy=nan_policy), expected)
+
+    def test_nan_policy_raise(self):
+        x = np.array([1.0, 2.0, np.nan, 3.0])
+        with pytest.raises(ValueError, match='input contains nan'):
+            variation(x, nan_policy='raise')
+
+    def test_bad_nan_policy(self):
+        with pytest.raises(ValueError, match='must be one of'):
+            variation([1, 2, 3], nan_policy='foobar')
+
+    def test_keepdims(self):
+        x = np.arange(10).reshape(2, 5)
+        y = variation(x, axis=1, keepdims=True)
+        expected = np.array([[np.sqrt(2)/2],
+                             [np.sqrt(2)/7]])
+        assert_allclose(y, expected)
+
+    @pytest.mark.parametrize('axis, expected',
+                             [(0, np.empty((1, 0))),
+                              (1, np.full((5, 1), fill_value=np.nan))])
+    def test_keepdims_size0(self, axis, expected):
+        x = np.zeros((5, 0))
+        y = variation(x, axis=axis, keepdims=True)
+        assert_equal(y, expected)
+
+    @pytest.mark.parametrize('incr, expected_fill', [(0, np.inf), (1, np.nan)])
+    def test_keepdims_and_ddof_eq_len_plus_incr(self, incr, expected_fill):
+        x = np.array([[1, 1, 2, 2], [1, 2, 3, 3]])
+        y = variation(x, axis=1, ddof=x.shape[1] + incr, keepdims=True)
+        assert_equal(y, np.full((2, 1), fill_value=expected_fill))
+
+    def test_propagate_nan(self):
+        # Check that the shape of the result is the same for inputs
+        # with and without nans, cf gh-5817
+        a = np.arange(8).reshape(2, -1).astype(float)
+        a[1, 0] = np.nan
+        v = variation(a, axis=1, nan_policy="propagate")
+        assert_allclose(v, [np.sqrt(5/4)/1.5, np.nan], atol=1e-15)
+
+    def test_axis_none(self):
+        # Check that `variation` computes the result on the flattened
+        # input when axis is None.
+        y = variation([[0, 1], [2, 3]], axis=None)
+        assert_allclose(y, np.sqrt(5/4)/1.5)
+
+    def test_bad_axis(self):
+        # Check that an invalid axis raises np.AxisError.
+        x = np.array([[1, 2, 3], [4, 5, 6]])
+        with pytest.raises(np.AxisError):
+            variation(x, axis=10)
+
+    def test_mean_zero(self):
+        # Check that `variation` returns inf for a sequence that is not
+        # identically zero but whose mean is zero.
+        x = np.array([10, -3, 1, -4, -4])
+        y = variation(x)
+        assert_equal(y, np.inf)
+
+        x2 = np.array([x, -10*x])
+        y2 = variation(x2, axis=1)
+        assert_equal(y2, [np.inf, np.inf])
+
+    @pytest.mark.parametrize('x', [np.zeros(5), [], [1, 2, np.inf, 9]])
+    def test_return_nan(self, x):
+        # Test some cases where `variation` returns nan.
+        y = variation(x)
+        assert_equal(y, np.nan)
+
+    @pytest.mark.parametrize('axis, expected',
+                             [(0, []), (1, [np.nan]*3), (None, np.nan)])
+    def test_2d_size_zero_with_axis(self, axis, expected):
+        x = np.empty((3, 0))
+        y = variation(x, axis=axis)
+        assert_equal(y, expected)
+
+    def test_neg_inf(self):
+        # Edge case that produces -inf: ddof equals the number of non-nan
+        # values, the values are not constant, and the mean is negative.
+        x1 = np.array([-3, -5])
+        assert_equal(variation(x1, ddof=2), -np.inf)
+
+        x2 = np.array([[np.nan, 1, -10, np.nan],
+                       [-20, -3, np.nan, np.nan]])
+        assert_equal(variation(x2, axis=1, ddof=2, nan_policy='omit'),
+                     [-np.inf, -np.inf])
+
+    @pytest.mark.parametrize("nan_policy", ['propagate', 'omit'])
+    def test_combined_edge_cases(self, nan_policy):
+        x = np.array([[0, 10, np.nan, 1],
+                      [0, -5, np.nan, 2],
+                      [0, -5, np.nan, 3]])
+        y = variation(x, axis=0, nan_policy=nan_policy)
+        assert_allclose(y, [np.nan, np.inf, np.nan, np.sqrt(2/3)/2])
+
+    @pytest.mark.parametrize(
+        'ddof, expected',
+        [(0, [np.sqrt(1/6), np.sqrt(5/8), np.inf, 0, np.nan, 0.0, np.nan]),
+         (1, [0.5, np.sqrt(5/6), np.inf, 0, np.nan, 0, np.nan]),
+         (2, [np.sqrt(0.5), np.sqrt(5/4), np.inf, np.nan, np.nan, 0, np.nan])]
+    )
+    def test_more_nan_policy_omit_tests(self, ddof, expected):
+        # The slightly strange formatting in the follow array is my attempt to
+        # maintain a clean tabular arrangement of the data while satisfying
+        # the demands of pycodestyle.  Currently, E201 and E241 are not
+        # disabled by the `# noqa` annotation.
+        nan = np.nan
+        x = np.array([[1.0, 2.0, nan, 3.0],
+                      [0.0, 4.0, 3.0, 1.0],
+                      [nan, -.5, 0.5, nan],
+                      [nan, 9.0, 9.0, nan],
+                      [nan, nan, nan, nan],
+                      [3.0, 3.0, 3.0, 3.0],
+                      [0.0, 0.0, 0.0, 0.0]])
+        v = variation(x, axis=1, ddof=ddof, nan_policy='omit')
+        assert_allclose(v, expected)
+
+    def test_variation_ddof(self):
+        # test variation with delta degrees of freedom
+        # regression test for gh-13341
+        a = np.array([1, 2, 3, 4, 5])
+        nan_a = np.array([1, 2, 3, np.nan, 4, 5, np.nan])
+        y = variation(a, ddof=1)
+        nan_y = variation(nan_a, nan_policy="omit", ddof=1)
+        assert_allclose(y, np.sqrt(5/2)/3)
+        assert y == nan_y