`scipy.stats._continuous_distns:ksone_gen`

source: /scipy/stats/_continuous_distns.py :104

Signature

   class     ksone_gen (    momtype    =  1   ,    a    =  None   ,    b    =  None   ,    xtol    =  1e-14   ,    badvalue    =  None   ,    name    =  None   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

Kolmogorov-Smirnov one-sided test statistic distribution.

Extended Summary

This is the distribution of the one-sided Kolmogorov-Smirnov (KS) statistics $D_{n}^{+}$ and $D_{n}^{-}$ for a finite sample size n >= 1 (the shape parameter).

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Notes

$D_{n}^{+}$ and $D_{n}^{-}$ are given by

D_{n}^{+} D_{n}^{-} = sup_{x} (F_{n} (x) - F (x)), = sup_{x} (F (x) - F_{n} (x)),

where $F$ is a continuous CDF and $F_{n}$ is an empirical CDF. ksone describes the distribution under the null hypothesis of the KS test that the empirical CDF corresponds to $n$ i.i.d. random variates with CDF $F$ .

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Examples

import numpy as np
from scipy.stats import ksone
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)

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Display the probability density function (``pdf``):

n = 1e+03
x = np.linspace(ksone.ppf(0.01, n),
                ksone.ppf(0.99, n), 100)

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ax.plot(x, ksone.pdf(x, n),
        'r-', lw=5, alpha=0.6, label='ksone pdf')

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Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a "frozen" RV object holding the given parameters fixed. Freeze the distribution and display the frozen ``pdf``:

rv = ksone(n)

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ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
ax.legend(loc='best', frameon=False)

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plt.show()

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Check accuracy of ``cdf`` and ``ppf``:

vals = ksone.ppf([0.001, 0.5, 0.999], n)
np.allclose([0.001, 0.5, 0.999], ksone.cdf(vals, n))

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Aliases

scipy.stats._continuous_distns.ksone_gen