TITLE:
Higher-Order Expansions of Sample Range from the Skew-t-Normal Distribution
AUTHORS:
Wanrou Yang
KEYWORDS:
Higher-Order Expansion, Skew-t-Normal Distribution, Rate of Convergence, Sample Range
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
20,
2025
ABSTRACT: For an independent and identically distributed skew-t-normal random sequence, this paper establishes the limit distribution of normalized sample range
M
n
−
m
n
. Based on the optimal normalized constants, the higher-order asymptotic expansion of the distribution function of sample range
M
n
−
m
n
is further derived, and its convergence rate is given. In addition, the approximate accuracy between the empirical value and the asymptotic theoretical value is systematically compared by numerical simulation.