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scipy.stats.

# kurtosistest

scipy.stats.kurtosistest(a, axis=0, nan_policy='propagate', alternative='two-sided', *, keepdims=False)

  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. Must contain at least five observations.

    axisint 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

      Added in version 1.7.0.

    keepdimsbool, 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:
    statisticfloat

      The computed z-score for this test.

    pvaluefloat

      The p-value for the hypothesis test.

  See also

  Kurtosis test

    Extended example

  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`.

  `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 | ⚠️ no JIT | ⚠️ no JIT
  Dask | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  References

  [1]

  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)

  For a more detailed example, see Kurtosis test.