Asymptotic Properties Of Extremes From Generalized Gamma Distribution And Logarithmic General Error Distribution

For a generalized gamma random sequence, with an optimal choice of nor-malizing constants, the asymptotic properties of distributions and densities of the normalized partial maxima are derived, and for a logarithmic general error random sequence, the asymptotic expansions of densities and moments of the normalized par-tial maxima are studied under two different kinds of normalizing constants, which consist of the contents of this thesis.For the first part of this thesis, by the probability density function of generalized gamma distribution, we derive some preliminary properties such as Mills equalities and Mills ratio. Hence, we get its distributional tail representation and the opti-mal normalizing constants. Furthermore, with optimal normalizing constants, the higher-order asymptotic expansions for distributions and densities of normalized partial maximum from the generalized gamma distribution are derived, by which we deduce its associated convergence rates of the distribution and the density of the extreme to the Gumbel extreme value distribution and the density of Gumbel extreme value distribution, respectively.In the second part, based on the asymptotic expansions for distributions of extremes from the logarithmic general error distribution, we derive its asymptotic expansions of the densities and the moments of normalized partial maxima under two different kinds of normalizing constants. A byproduct is to deduce the convergence rates of the densities and the moments of normalized maxima to the densities and the moments of the corresponding extreme value distribution, respectively.