Asymptotic Properties Of Extreme From The Short-tailed Symmetric Distribution

In this paper,we focus on the higher-order expansion of probability distribu-tion function of the normalized maximum from short-tailed symmetric distribution under linear and power normalization,and also the convergence rates of the mo-ments of normalized maximum to the moments of the corresponding extreme value distribution.There are three parts in this thesis.In the first part,the tail expression of the distribution is deduced according to the probability density function of the short-tailed symmetric distribution first-ly.Then the extreme distribution type of the distribution is determined.Hence we establish the higher-order expansion of probability distribution function of the normalized maximum from short-tailed symmetric distribution under linear normal-ization.In the second part,we establish the higher-order expansion of probability dis-tribution function of the normalized maximum from short-tailed symmetric distri-bution under power normalization by the similar method.In the last part,based on the asymptotic expansions for distributions of ex-tremes and the definition of moments,we derive the convergence rates of the mo-ments of normalized maximum to the moments of the corresponding extreme value distribution.