statsmodels.stats.stattools.robust_kurtosis¶

statsmodels.stats.stattools.robust_kurtosis(y, axis=0, ab=(5.0, 50.0), dg=(2.5, 25.0), excess=True)[source]¶

Calculates the four kurtosis measures in Kim & White

Parameters:

yarray_like: Data to compute use in the estimator.
axisint or None, optional: Axis along which the kurtosis are computed. If None, the entire array is used.
a iterable, optional: Contains 100*(alpha, beta) in the kr3 measure where alpha is the tail quantile cut-off for measuring the extreme tail and beta is the central quantile cutoff for the standardization of the measure
dbiterable, optional: Contains 100*(delta, gamma) in the kr4 measure where delta is the tail quantile for measuring extreme values and gamma is the central quantile used in the the standardization of the measure
excessbool, optional: If true (default), computed values are excess of those for a standard normal distribution.

Returns:

kr1ndarray: The standard kurtosis estimator.
kr2ndarray: Kurtosis estimator based on octiles.
kr3ndarray: Kurtosis estimators based on exceedance expectations.
kr4ndarray: Kurtosis measure based on the spread between high and low quantiles.

Notes

The robust kurtosis measures are defined

K R_{2} = \frac{({\hat{q}}_{.875} - {\hat{q}}_{.625}) + ({\hat{q}}_{.375} - {\hat{q}}_{.125})}{{\hat{q}}_{.75} - {\hat{q}}_{.25}}

K R_{3} = \frac{\hat{E} (y | y > {\hat{q}}_{1 - α}) - \hat{E} (y | y < {\hat{q}}_{α})}{\hat{E} (y | y > {\hat{q}}_{1 - β}) - \hat{E} (y | y < {\hat{q}}_{β})}

K R_{4} = \frac{{\hat{q}}_{1 - δ} - {\hat{q}}_{δ}}{{\hat{q}}_{1 - γ} - {\hat{q}}_{γ}}

where ${\hat{q}}_{p}$ is the estimated quantile at $p$ .