Higher-order expansions of sample range from skew-normal distribution

W{X-n, n >= 1} is a sequence of i.i.d. random variables with common skew-normal distribution, the limiting distribution of normalized sample range M-n - m(n) was established in this paper, where M-n and m(n) are the partial maximum and minimum of {X-n, n >= 1}, respectively. Meanwhile, higher-order expansions of sample range distribution and the rates of convergence to the limits are derived with optimal normalizing constants. Numerical analysis is given to compare the accuracy of the actual values with their asymptotics and illustrate the theoretical findings.