statsmodels
ENH: hypothesis test for heavy tails, deviation from normality
We don't have much specifically for checking tail behavior of distributions.
Would be useful to check whether we might run into estimation problems because of observations with large deviations because of outliers or heavy tails/
I found it in minitab technical pater Appendix E as "SJ test"
test statistic is based on ratio standard deviation over mean absolute deviation from median (like a mean MAD version). Distribution is normal, and Gel et al use onesided test for heavier than normal tails. We could also test for lighter than normal tails.
I guess the usage would be similar to the kurtosis test for normality. I don't think we or scipy hase a one-sided test for that.
Gel, Yulia R., Weiwen Miao, and Joseph L. Gastwirth. 2007. “Robust Directed Tests of Normality against Heavy-Tailed Alternatives.” Computational Statistics & Data Analysis 51 (5): 2734–46. https://doi.org/10.1016/j.csda.2006.08.022.
minitab technical paper https://support.minitab.com/en-us/minitab/18/Assistant_One_Sample_Variance.pdf
Note: I don't remember, but I might have seen something similar with IQR, which different quantiles. Maybe it was a different context with order statistics, quantiles and L-moments.
