Geometric and statistical curvatures of the skew-t distributions and their application

Qiaoyan Wu and Hongchang Hu

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 20, 6428-6442

Abstract: It is common to compare the p-value to some standard threshold (e.g., α= 0.01 or 0.05 or 0.10). However, in many practical problems, this approach is not necessarily reasonable. We investigate geometric curvature for the skew-t distribution family, and obtain the threshold x* corresponds to the point of maximum geometric curvature in the probability density function of the skew-t distribution. Furthermore, we calculate p(x∗)=P(X≤x∗) (p(x∗)=P(X≥x∗)), and utilize it to denote the one-tailed significance level. The study further investigates the statistical curvature characteristics of the skew-t distribution family and addresses the minimum sample size issue. This ensures the nearly validity of inferring the distribution based on linear approximations to the log likelihood function. Additionally, a practical application is provided to demonstrate the method’s rationality.

Date: 2025
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DOI: 10.1080/03610926.2025.2457494

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