scipy.stats.ksone#

scipy.stats.ksone = <scipy.stats._continuous_distns.ksone_gen object>[source]#

Kolmogorov-Smirnov one-sided test statistic distribution.

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

As an instance of the rv_continuous class, ksone object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods

rvs(n, loc=0, scale=1, size=1, random_state=None)

Random variates.

pdf(x, n, loc=0, scale=1)

Probability density function.

logpdf(x, n, loc=0, scale=1)

Log of the probability density function.

cdf(x, n, loc=0, scale=1)

Cumulative distribution function.

logcdf(x, n, loc=0, scale=1)

Log of the cumulative distribution function.

sf(x, n, loc=0, scale=1)

Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).

logsf(x, n, loc=0, scale=1)

Log of the survival function.

ppf(q, n, loc=0, scale=1)

Percent point function (inverse of cdf — percentiles).

isf(q, n, loc=0, scale=1)

Inverse survival function (inverse of sf).

moment(order, n, loc=0, scale=1)

Non-central moment of the specified order.

stats(n, loc=0, scale=1, moments=’mv’)

Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).

entropy(n, loc=0, scale=1)

(Differential) entropy of the RV.

fit(data)

Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.

expect(func, args=(n,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)

Expected value of a function (of one argument) with respect to the distribution.

median(n, loc=0, scale=1)

Median of the distribution.

mean(n, loc=0, scale=1)

Mean of the distribution.

var(n, loc=0, scale=1)

Variance of the distribution.

std(n, loc=0, scale=1)

Standard deviation of the distribution.

interval(confidence, n, loc=0, scale=1)

Confidence interval with equal areas around the median.

See also

kstwobign, kstwo, kstest

Notes

Dn+ and Dn are given by

Dn+=supx(Fn(x)F(x)),Dn=supx(F(x)Fn(x)),

where F is a continuous CDF and Fn 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.

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, ksone.pdf(x, n, loc, scale) is identically equivalent to ksone.pdf(y, n) / scale with y = (x - loc) / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.

References

[1]

Birnbaum, Z. W. and Tingey, F.H. “One-sided confidence contours for probability distribution functions”, The Annals of Mathematical Statistics, 22(4), pp 592-596 (1951).

Examples

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

Display the probability density function (pdf):

>>> n = 1e+03
>>> x = np.linspace(ksone.ppf(0.01, n),
...                 ksone.ppf(0.99, n), 100)
>>> ax.plot(x, ksone.pdf(x, n),
...         'r-', lw=5, alpha=0.6, label='ksone pdf')

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)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
../../_images/scipy-stats-ksone-1_00_00.png

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))
True