TITLE:
Higher-Order Expansions of Sample Range from Skew-t Distribution
AUTHORS:
Xinyu Luo
KEYWORDS:
Skew-t Distribution, Sample Range, Extreme Value Theory, Higher-Order Asymptotic Expansion, Limiting Distribution, Heavy-Tailed Distribution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.8,
August
21,
2026
ABSTRACT: The sample range is an important statistic in extreme value theory and has been widely used to characterize the variability of extreme observations. However, the asymptotic behavior of the sample range for asymmetric heavy-tailed distributions remains insufficiently studied. In this paper, we investigate the limiting distribution and higher-order asymptotic expansions of the sample range derived from the skew-t distribution. Specifically, for a sequence of independent and identically distributed skew-t random variables, we first establish the limiting distribution of the normalized sample range by combining the asymptotic behaviors of the sample maximum and minimum. Then, based on refined tail expansions of the skew-t distribution, we derive the second-order and third-order asymptotic expansions of the normalized range under different conditions of the degrees-of-freedom parameter. These expansions provide explicit corrections to the first-order limiting approximation and reveal the influence of skewness and tail heaviness on finite-sample deviations. Furthermore, Monte Carlo simulations are conducted to evaluate the accuracy of the proposed approximations.