scipy.stats.VonMises.

skewness#

VonMises.skewness(*, method=None)[source]#

Skewness, a measure of asymmetry

For real-line distributions, the skewness is the standardized third moment.

The skewness \(\nu\) of a circular random variable \(X\) is defined ([2] 31) as

\[s = \frac{ \bar{\beta}_2 } {(1 - \rho)^{3/2}}\]

where \(\rho\) and \(\bar{\beta}_2\) are the real and imaginary components of the first and second central trigonometric moments of \(X\), respectively.

Parameters:

method{None, ‘formula’, ‘general’, ‘transform’, ‘normalize’, ‘cache’}: Method used to calculate the standardized third moment. Not all methods are available for all distributions. See moment for details.

See also

moment
mean
variance

References

[1]

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

[2]

Mardia, Kanti V., and Peter E. Jupp. Directional statistics. John Wiley & Sons, 1999. DOI:10.1002/9780470316979.

Examples

Instantiate a distribution with the desired parameters:

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

Evaluate the skewness:

>>> X.skewness()
0.0
>>> X.skewness() == X.moment(order=3, kind='standardized')
True