statsmodels
ENH: inference for skew and kurtosis without normality assumption
I finally found inference for skew and kurtosis for nonnormal distributions
Bao 2013 looks good Pewsey 2005 seems to be the first to derive the distribution for kurtosis Mahmoudi et al don't cite Pewsey nor Bao
Bao, Yong. 2013. “On Sample Skewness and Kurtosis.” Econometric Reviews 32 (4): 415–48. https://doi.org/10.1080/07474938.2012.690665.
Mahmoudi, Mohammad Reza, Bui Anh Tuan, and Kim-Hung Pho. 2021. “On Kurtoses of Two Symmetric or Asymmetric Populations.” Journal of Computational and Applied Mathematics 391 (August): 113370. https://doi.org/10.1016/j.cam.2020.113370.
Pewsey, Arthur. 2005. “The Large-Sample Distribution of the Most Fundamental of Statistical Summaries.” Journal of Statistical Planning and Inference 134 (2): 434–44. https://doi.org/10.1016/j.jspi.2004.04.014.
variance for kurtosis needs 8th moment So, it will only be useful in large samples. But, if we get a rough confidence interval for kurtosis, then we can guess on the reliability of inference for variance #8261
