statsmodels.stats.stattools.robust_skewness

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

Calculates the four skewness measures in Kim & White

Parameters

yarray_like

Data to compute use in the estimator.

axisint or None, optional

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

Returns

sk1ndarray

The standard skewness estimator.

sk2ndarray

Skewness estimator based on quartiles.

sk3ndarray

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

sk4ndarray

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.