robust_kurtosis(y, axis=0, ab=(5.0, 50.0), dg=(2.5, 25.0), excess=True)¶
Calculates the four kurtosis measures in Kim & White
y : array-like
axis : int or None, optional
Axis along which the kurtoses are computed. If None, the entire array is used.
ab: 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
db: iterable, 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
excess : bool, optional
If true (default), computed values are excess of those for a standard normal distribution.
kr1 : ndarray
The standard kurtosis estimator.
kr2 : ndarray
Kurtosis estimator based on octiles.
kr3 : ndarray
Kurtosis estimators based on exceedence expectations.
kr4 : ndarray
Kurtosis measure based on the spread between high and low quantiles.
The robust kurtosis measures are defined
where is the estimated quantile at .
[R58] Tae-Hwan Kim and Halbert White, “On more robust estimation of skewness and kurtosis,” Finance Research Letters, vol. 1, pp. 56-73, March 2004.