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Contents of PMS, Vol. 43, Fasc. 2,
pages 165 - 184
DOI: 10.37190/0208-4147.00129
Published online 20.10.2023
 

Uniform convergence rates of skew-normal extremes

Qian Xiong
Zuoxiang Peng
Saralees Nadarajah

Uniform Convergence of Skew-Normal Extremes

Let Mn=max(X1,…,Xn) 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 an−1(Mn−bn) to its ultimate extreme value distribution is proportional to 12.

2010 AMS Mathematics Subject Classification: Primary 60G70; Secondary 60F05.

Keywords and phrases: extreme value distribution, rate of uniform convergence, skew-normal distribution.

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