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cramervonmises(rvs, cdf, args=())

This performs a test of the goodness of fit of a cumulative distribution function (cdf) F compared to the empirical distribution function F_n of observed random variates X_1, ..., X_n that are assumed to be independent and identically distributed (). The null hypothesis is that the X_i have cumulative distribution F.

Notes

The p-value relies on the approximation given by equation 1.8 in . It is important to keep in mind that the p-value is only accurate if one tests a simple hypothesis, i.e. the parameters of the reference distribution are known. If the parameters are estimated from the data (composite hypothesis), the computed p-value is not reliable.

Parameters

rvs : array_like: A 1-D array of observed values of the random variables X_i.
cdf : str or callable: The cumulative distribution function F to test the observations against. If a string, it should be the name of a distribution in scipy.stats. If a callable, that callable is used to calculate the cdf: cdf(x, *args) -> float.
args : tuple, optional: Distribution parameters. These are assumed to be known; see Notes.

Returns

res : object with attributes

statistic: statistic
pvalue: pvalue

Perform the one-sample Cramér-von Mises test for goodness of fit.

Examples

Suppose we wish to test whether data generated by ``scipy.stats.norm.rvs`` were, in fact, drawn from the standard normal distribution. We choose a significance level of alpha=0.05.

import numpy as np
from scipy import stats
rng = np.random.default_rng()
x = stats.norm.rvs(size=500, random_state=rng)
res = stats.cramervonmises(x, 'norm')
res.statistic, res.pvalue

The p-value 0.79 exceeds our chosen significance level, so we do not reject the null hypothesis that the observed sample is drawn from the standard normal distribution.

Now suppose we wish to check whether the same samples shifted by 2.1 is consistent with being drawn from a normal distribution with a mean of 2.

y = x + 2.1
res = stats.cramervonmises(y, 'norm', args=(2,))
res.statistic, res.pvalue

Here we have used the `args` keyword to specify the mean (``loc``) of the normal distribution to test the data against. This is equivalent to the following, in which we create a frozen normal distribution with mean 2.1, then pass its ``cdf`` method as an argument.

frozen_dist = stats.norm(loc=2)
res = stats.cramervonmises(y, frozen_dist.cdf)
res.statistic, res.pvalue

In either case, we would reject the null hypothesis that the observed sample is drawn from a normal distribution with a mean of 2 (and default variance of 1) because the p-value 0.04 is less than our chosen significance level.

See :

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GitHub : /scipy/stats/_hypotests.py#483
type: <class 'function'>
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Notes

Parameters

Returns

See Also

Examples

Local connectivity graph