scipy.stats.Normal.

kurtosis#

Normal.kurtosis(*, method=None, convention='non-excess')[source]#

Kurtosis (standardized fourth moment)

By default, this is the standardized fourth moment, also known as the “non-excess” or “Pearson” kurtosis (e.g. the kurtosis of the normal distribution is 3). The “excess” or “Fisher” kurtosis (the standardized fourth moment minus 3) is available via the convention parameter.

Parameters:

method{None, ‘formula’, ‘general’, ‘transform’, ‘normalize’, ‘cache’}

Method used to calculate the standardized fourth moment. Not all methods are available for all distributions. See moment for details.

convention{‘non-excess’, ‘excess’}

Two distinct conventions are available:

'non-excess': the standardized fourth moment (Pearson’s kurtosis)
'excess': the standardized fourth moment minus 3 (Fisher’s kurtosis)

The default is 'non-excess'.

See also

moment
mean
variance

References

[1]

Kurtosis, Wikipedia, https://en.wikipedia.org/wiki/Kurtosis

Examples

Instantiate a distribution with the desired parameters:

>>> from scipy import stats
>>> X = stats.Normal(mu=1., sigma=2.)

Evaluate the kurtosis:

>>> X.kurtosis()
3.0
>>> (X.kurtosis()
...  == X.kurtosis(convention='excess') + 3.
...  == X.moment(order=4, kind='standardized'))
True