Calculates the four kurtosis measures in Kim & White
Parameters: | y : array-like axis : int or None, optional
ab: iterable, optional :
db: iterable, optional :
excess : bool, optional
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Returns: | kr1 : ndarray
kr2 : ndarray
kr3 : ndarray
kr4 : ndarray
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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.
[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. |