statsmodels.stats.stattools.robust_skewness

statsmodels.stats.stattools.robust_skewness(y, axis=0)

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

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

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

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

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