3.11.20.2.7. 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

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

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

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

[R85]

Tae-Hwan Kim and Halbert White, “On more robust estimation of

skewness and kurtosis,” Finance Research Letters, vol. 1, pp. 56-73, March 2004.