Asymptotic Expansions Of Extremes From Inverse Gaussian Distribution

In this thesis,the asymptotic expansions of distribution of extremes from inverse gaussian distribution under two kinds of different normalized constant are discussed.The higher-order distribution and density expansions of powered order statistics from inverse gaussian distribution under normalized constant are also obtained.The article is mainly divided into three parts:For the first part of this article,based on the asymptotic expansion of the maximum distribution from the inverse Gaussian distribution,the convergence rate of the maximum distribution to the Gumbel distribution under two different kinds of normalized constants is obtained.In the second part,the higher-order distribution and density expansions of powered order statistics are derived.The convergence rate of powered order statistics to?_r(x) and the convergence rate of density powered order statistics converging to corresponding extreme density are also obtained.In the third part,based on the theorems proved by the first two parts,numeri-cal simulation analysis are given.The effect of asymptotic expansion of the inverse gaussian distribution is judged by comparing actual values,first-order asymptotic,second-order asymptotic and third-order asymptotic.