scipy.stats.kurtosis

scipy.stats.kurtosis(a, axis=0, fisher=True, bias=True, nan_policy='propagate')

Compute the kurtosis (Fisher or Pearson) of a dataset.

Kurtosis is the fourth central moment divided by the square of the variance. If Fisher’s definition is used, then 3.0 is subtracted from the result to give 0.0 for a normal distribution.

If bias is False then the kurtosis is calculated using k statistics to eliminate bias coming from biased moment estimators

Use kurtosistest to see if result is close enough to normal.

Parameters:

a : array

data for which the kurtosis is calculated

axis : int or None, optional

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

fisher : bool, optional

If True, Fisher’s definition is used (normal ==> 0.0). If False, Pearson’s definition is used (normal ==> 3.0).

bias : bool, optional

If False, then the calculations are corrected for statistical bias.

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

Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’.

Returns:

kurtosis : array

The kurtosis of values along an axis. If all values are equal, return -3 for Fisher’s definition and 0 for Pearson’s definition.

References

[R627]

Zwillinger, D. and Kokoska, S. (2000). CRC Standard Probability and Statistics Tables and Formulae. Chapman & Hall: New York. 2000.

Examples

>>> from scipy.stats import kurtosis
>>> kurtosis([1, 2, 3, 4, 5])
-1.3