Limit Distributions And Asymptotic Expansions Of Distributions Of Extremes From Skew Normal-Logistic Distribution

This thesis studies the tail properties, extreme value distribution and its asymptotic expansion of distribution of the maximum of skew normal-logistic distribution. The paper is divided into two main parts.In the first part, we establish the Mills-type inequality and Mills-type ratio of skew normal-logistic distribution, and derive its tail representation which shows that the lim-iting distributions of normalized maximum and minimum from the skew normal-logistic distribution are A(x) and H3(x) respectively. The norming constants are also obtained, and we establish the pointwise convergence rate of distribution of maximum to its ex-treme value distribution. This part also considers the tail behavior and limit distribution of maximum on finite mixed skew normal-logistic distribution.In the second part, we further refine the tail behavior of the skew normal-logistic dis-tribution and derive the asymptotic expansion of distribution of its normalized maximum, from which we deduce the pointwise convergence rate of the distribution of its maximum.