Author(s)

Wanrou Yang

School of Mathematics and Statistics, Southwest University, Chongqing, China.

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.

Higher-Order Expansion, Skew-t-Normal Distribution, Rate of Convergence, Sample Range

Yang, W. (2025) Higher-Order Expansions of Sample Range from the Skew-t-Normal Distribution. Journal of Applied Mathematics and Physics, 13, 3975-3988. doi: 10.4236/jamp.2025.1311222.