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¶

Data to compute use in the estimator.

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

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

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

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