statsmodels
ENH: Inference for quantile measures of kurtosis, peakedness, and tail weight
(mainly to park a reference for now)
We have quantile based measures for skew and kurtosis (relative to normal distribution)
Here is an article that includes confidence intervals and references to other inference. (I only did very partial skimming)
Robert G. Staudte (2017) Inference for quantile measures of kurtosis, peakedness, and tail weight, Communications in Statistics - Theory and Methods, 46:7, 3148-3163, https://doi.org/10.1080/03610926.2015.1056366
related: including kurtosis to make variance tests more robust to distributional assumptions
#8261 #7235 #6566
one good feature to have would be a 3-valued classification by different measures e.g. negative, around zero and large positive excess kurtosis, (I never remember the latin names like leptokurtic, ....) and same for skew
For benett test in #8261, minitab uses tail heaviness/kurtosis classification to warn about minimum sample size requirements
for extreme value theory we have tail order as a more specific criterion, e.g. #7472
just an idea
We might be able to use this as a diagnostic tool for comparing predictive distribution with observed distribution. e.g. for Poisson
- we currently have pmf observed and expected averaged over sample
- we have specific statistics, tests for zero inflation
- we have excess dispersion measure for over or under dispersion
- we have diagnostic plots for pmf, cdf (probplots)
- but we don't have classification for other kind of deviations, e.g. outliers, heavy tails, ....
The idea would be to compute the quantile measures on the predictive cdf and compare it with the observed cdf.