Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(3): 679-698

Online first article May 3, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b160526

Copyright © The Korean Mathematical Society.

On asymptotic of extremes from generalized Maxwell distribution

Jianwen Huang, Jianjun Wang

Southwest University, Southwest University

Abstract

In this paper, with optimal normalized constants, the asymptotic expansions of the distribution and density of the normalized maxima from generalized Maxwell distribution are derived. For the distributional expansion, it shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to $1/\log n.$ For the density expansion, on the one hand, the main result is applied to establish the convergence rate of the density of extreme to its limit. On the other hand, the main result is applied to obtain the asymptotic expansion of the moment of maximum.

Keywords: density, expansion, extreme value distribution, generalized Maxwell distribution, moment

MSC numbers: Primary 62E20, 60G70; Secondary 60F15, 60F05