On asymptotic of extremes from generalized Maxwell distribution
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 679-698
https://doi.org/10.4134/BKMS.b160526
Published online May 31, 2018
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
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