scipy.stats.kurtosistest#

scipy.stats.kurtosistest(a, axis=0, nan_policy='propagate', alternative='two-sided')[source]#

Test whether a dataset has normal kurtosis.

This function tests the null hypothesis that the kurtosis of the population from which the sample was drawn is that of the normal distribution.

Parameters:
aarray

Array of the sample data.

axisint or None, optional

Axis along which to compute test. Default is 0. If None, compute over the whole array a.

nan_policy{‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. The following options are available (default is ‘propagate’):

  • ‘propagate’: returns nan

  • ‘raise’: throws an error

  • ‘omit’: performs the calculations ignoring nan values

alternative{‘two-sided’, ‘less’, ‘greater’}, optional

Defines the alternative hypothesis. The following options are available (default is ‘two-sided’):

  • ‘two-sided’: the kurtosis of the distribution underlying the sample is different from that of the normal distribution

  • ‘less’: the kurtosis of the distribution underlying the sample is less than that of the normal distribution

  • ‘greater’: the kurtosis of the distribution underlying the sample is greater than that of the normal distribution

New in version 1.7.0.

Returns:
statisticfloat

The computed z-score for this test.

pvaluefloat

The p-value for the hypothesis test.

Notes

Valid only for n>20. This function uses the method described in [1].

References

[1]

see e.g. F. J. Anscombe, W. J. Glynn, “Distribution of the kurtosis statistic b2 for normal samples”, Biometrika, vol. 70, pp. 227-234, 1983.

Examples

>>> import numpy as np
>>> from scipy.stats import kurtosistest
>>> kurtosistest(list(range(20)))
KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.08804338332528348)
>>> kurtosistest(list(range(20)), alternative='less')
KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.04402169166264174)
>>> kurtosistest(list(range(20)), alternative='greater')
KurtosistestResult(statistic=-1.7058104152122062, pvalue=0.9559783083373583)

>>> rng = np.random.default_rng()
>>> s = rng.normal(0, 1, 1000)
>>> kurtosistest(s)
KurtosistestResult(statistic=-1.475047944490622, pvalue=0.14019965402996987)