Limit Properties Of Extreme From Asymmetric Normal Distribution And Generalized Gamma Distribution

For a asymmetric normal random sequence and a generalized gamma random sequence,under an optimal choice of normalizing constants,the asymptotic prop-erties of distribution of the normalized partial maxima are derived,the asymptotic behaviour of observations near the parital maxima and the sum of such observations are also studied.This paper is mainly divided into two parts.In the first part,some fundamental but important properties are derived ac-cording to the probability density.Such as Mills ratio and the tail representation.Then,the extreme value distribution type of this distribution can be estimated to determine the optimal normalizing constants,the higher-order asymptotic expan-sions for distributions of normalized partial maximum from the asymmetric normal distribution and its associated convergence rates of the distribution of the extreme to its extreme value distribution are dervied.What's more,the distribution which is svelte can be determined according to the properties of asymmetric normal dis-tribution.With the distribution of obsversations near the partial maxima and the sum of such observations weakly converges to an expontial distribution,the optimal normalizing constants are derived respectively.In the second part,the higher-order expansions of cumulative distribution func-tion of maximum from the generalized gamma distribution and its associated con-vergence rates of the distribution of the extreme to its corresponding extreme value distribution are established under power normalization.And then,the distribution which is svelte is determined by the properties of generalized gamma distribution.With the distribution of obsversations near the partial maxima and the sum of such observations weakly converges to an expontial distribution,the optimal normalizing constants are derived,respectively.