Asymptotic Expansions Of Extremes From Logarithmic General Maxwell Distribution

In this thesis,we mainly discuss asymptotic expansions of density of extremes from logarithmic generalized maxwell distribution under two kinds of different nor-malized constant.The asymptotic expansions of extremes and the density of extreme from logarithmic generalized maxwell distribution under the power normalization are also obtained.For the first part of this thesis,based on the asymptotic expansion for distribu-tion of extremes from the logarithmic generalized maxwell distribution,we obtained the asymptotic expansions of the densities of normalized partial maxima under two different kinds of normalized constants.A byproduct is to deduce the convergence rates of the densities of normalized maxima to the densities of its extreme value distribution.The second part,based on the tail representation of the logarithmic general-ized maxwell distribution and the asymptotic expansion for distribution of extremes under power normalized constants,we obtained the asymptotic expansion for dis-tribution of extremes and the asymptotic expansion of density of extremes from the logarithmic generalized maxwell distribution under power normalization.A byprod-uct is to deduce the convergence rates of distribution of extremes and the densities to ?1(x)and the density of its extreme value distribution.