statsmodels.stats.stattools.robust_skewness¶

statsmodels.stats.stattools.robust_skewness(y, axis=0)[source]¶

Calculates the four skewness measures in Kim & White

Parameters:

y : array-like

axis : int or None, optional

Axis along which the skewness measures are computed. If None, the entire array is used.

Returns:

sk1 : ndarray

The standard skewness estimator.

sk2 : ndarray

Skewness estimator based on quartiles.

sk3 : ndarray

Skewness estimator based on mean-median difference, standardized by absolute deviation.

sk4 : ndarray

Skewness estimator based on mean-median difference, standardized by standard deviation.

Notes

The robust skewness measures are defined

$SK_{2}=\frac{\left(q_{.75}-q_{.5}\right) -\left(q_{.5}-q_{.25}\right)}{q_{.75}-q_{.25}}$

$SK_{3}=\frac{\mu-\hat{q}_{0.5}} {\hat{E}\left[\left|y-\hat{\mu}\right|\right]}$

$SK_{4}=\frac{\mu-\hat{q}_{0.5}}{\hat{\sigma}}$

[R59]

Tae-Hwan Kim and Halbert White, “On more robust estimation of skewness and kurtosis,” Finance Research Letters, vol. 1, pp. 56-73, March 2004.