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.
- axis
intorNone,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:
Notes
The robust kurtosis measures are defined
\[KR_{2}=\frac{\left(\hat{q}_{.875}-\hat{q}_{.625}\right) +\left(\hat{q}_{.375}-\hat{q}_{.125}\right)} {\hat{q}_{.75}-\hat{q}_{.25}}\]\[KR_{3}=\frac{\hat{E}\left(y|y>\hat{q}_{1-\alpha}\right) -\hat{E}\left(y|y<\hat{q}_{\alpha}\right)} {\hat{E}\left(y|y>\hat{q}_{1-\beta}\right) -\hat{E}\left(y|y<\hat{q}_{\beta}\right)}\]\[KR_{4}=\frac{\hat{q}_{1-\delta}-\hat{q}_{\delta}} {\hat{q}_{1-\gamma}-\hat{q}_{\gamma}}\]where \(\hat{q}_{p}\) is the estimated quantile at \(p\).