Uniform convergence rates of skew-normal extremes
Qian Xiong
Zuoxiang Peng
Saralees Nadarajah
Uniform Convergence of Skew-Normal Extremes
Let \( M_n = \max(X_1, \ldots, X_n) \) denote the partial maximum of an independent and identically distributed skew-normal random sequence.
In this paper, the rate of uniform convergence of skew-normal extremes is derived.
It is shown that with optimal normalizing constants, the convergence rate of \( a_n^{-1} \left(M_{n} - b_n\right) \) to its ultimate extreme value distribution is proportional to \(\frac{1}{2}\).
2010 AMS Mathematics Subject Classification: Primary 60G70; Secondary 60F05.
Keywords and phrases: extreme value distribution, rate of uniform convergence, skew-normal distribution.