Asymptotic Expansions On Powered-Order Statistics From Logarithmic General Maxwell Sequences

In this thesis,we mainly discuss asymptotic expansions of distribution and density of powered-order statistics from logarithmic general maxwell sequences under optimal normalizing constants.The uniform convergence of distribution of powered-order statistics from logarithmic general maxwell sequences and convergence for moments of powered-extremes from logarithmic general maxwell sequences are also obtained.For the first part of this thesis,based on the distributional tail representation for distribution of extremes from logarithmic generalized maxwell distribution,we obtained the asymptotic expansions of distribution and density of powered-order statistics from logarithmic general maxwell sequences under optimal normalizing constants.A byproduct is to deduce the convergence rates of the distribution and density of powered-order statistics from logarithmic general maxwell sequences to the distribution and density of the corresponding extreme value distribution.In second part,based on the distributional tail representation for distribution of extremes from the logarithmic generalized maxwell distribution,we obtained the uniform convergence of distribution of powered-order statistics from logarithmic general maxwell sequences.The last part,based on the asymptotic expansions of density of poweredextremes from logarithmic general maxwell sequences,we obtained the asymptotic expansion of moments of powered-extremes from logarithmic general maxwell sequences.A byproduct is to deduce the convergence rates of moments of poweredextremes from logarithmic general maxwell sequences to the moments of the corresponding extreme value distribution.