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 \(D_n^+\) and \(D_n^-\) for a finite sample size - n >= 1(the shape parameter).- As an instance of the - rv_continuousclass,- ksoneobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- Notes - \(D_n^+\) and \(D_n^-\) are given by \[\begin{split}D_n^+ &= \text{sup}_x (F_n(x) - F(x)),\\ D_n^- &= \text{sup}_x (F(x) - F_n(x)),\\\end{split}\]- where \(F\) is a continuous CDF and \(F_n\) is an empirical CDF. - ksonedescribes 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 - locand- scaleparameters. Specifically,- ksone.pdf(x, n, loc, scale)is identically equivalent to- ksone.pdf(y, n) / scalewith- 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()   - Check accuracy of - cdfand- ppf:- >>> vals = ksone.ppf([0.001, 0.5, 0.999], n) >>> np.allclose([0.001, 0.5, 0.999], ksone.cdf(vals, n)) True - 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.