`scipy.stats._stats_py:kurtosistest`

source: /scipy/stats/_stats_py.py :1701

Signature

   def     kurtosistest (    a    ,    axis    =  0   ,    nan_policy    =  propagate   ,    alternative    =  two-sided   ,  * ,     keepdims    =  False     )

Summary

Test whether a dataset has normal kurtosis.

Extended Summary

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

a : array

Array of the sample data. Must contain at least five observations.

axis : int or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.
raise: if a NaN is present, a ValueError will be raised.

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

keepdims : bool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

Returns

statistic : float: The computed z-score for this test.
pvalue : float: The p-value for the hypothesis test.

Notes

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

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

Array API Standard Support

kurtosistest has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

import numpy as np
from scipy.stats import kurtosistest

✓

kurtosistest(list(range(20)))
kurtosistest(list(range(20)), alternative='less')
kurtosistest(list(range(20)), alternative='greater')

✗

rng = np.random.default_rng()
s = rng.normal(0, 1, 1000)

✓

kurtosistest(s)

✗

For a more detailed example, see :ref:`hypothesis_kurtosistest`.

Aliases

scipy.stats.kurtosistest