混合偏t分布的极值理论

发布时间：2018-01-21 03:44

本文关键词： 混合偏t分布极值分布高阶展开式线性赋范幂赋范　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文将研究在线性赋范和幂赋范两种赋范定义下混合偏t分布极值的渐近性质及数值模拟,全文主要分为以下三个部分.第一部分研究在线性赋范和幂赋范两种条件下,混合偏t分布规范化最大值的分布函数的高阶渐近展开式.首先,应用偏t分布的尾部表达式可以得到混合偏t分布的尾部表达式,应用该尾部表达式可以判断出在线性赋范条件下混合偏t分布的极值分布类型,并且确定相应的最优规范化常数.其次,在该最优规范化常数条件下,通过对混合偏t分布尾部表达式的精确展开,得到在线性赋范条件下混合偏t分布规范化最大值的分布函数的高阶渐近展开式.最后,通过简单变形,得到在幂赋范条件下混合偏t分布规范化最大值的分布函数的高阶渐近展开式.第二部分研究在线性赋范和幂赋范两种条件下,混合偏t分布规范化最大值的密度函数的高阶渐近展开式.首先,应用偏t分布的密度函数的表达式得到混合偏t分布的密度函数的表达式.其次,分别利用第一部分得到的在线性赋范和幂赋范两种条件下规范化最大值的分布函数的高阶渐近展式以及混合偏t分布的密度函数的表达式,即可求得两种赋范条件下规范化最大值的密度函数的高阶渐近展开式.第三部分基于第一、二部分的结果进行数值模拟和比较.通过两个例子分别对规范化最大值的分布函数和密度函数的各阶渐近展式进行模拟,与相应的精确值进行比较,最后用图表的方式展示出来,进而更直观地反映线性赋范和幂赋范两种条件下高阶渐近展式拟合精度的差异.
[Abstract]:In this paper, the asymptotic properties and numerical simulation of the extreme value of mixed partial t distribution under the definitions of linear normed and power normed are studied. In the first part, we study the higher order asymptotic expansion of the distribution function of the normalized maximum value of the mixed partial t distribution under the condition of linear normed and power normed. The tail expression of mixed partial t distribution can be obtained by using the tail expression of partial t distribution, and the extreme distribution type of mixed partial t distribution can be determined under linear normed condition. And the corresponding optimal normalization constant is determined. Secondly, under the condition of the optimal normalization constant, the exact expansion of the tail expression of the mixed partial t distribution is carried out. The higher order asymptotic expansion of the distribution function of the normalized maximum value of the mixed partial t distribution under the condition of linear normed is obtained. Finally, the simple deformation is obtained. The higher order asymptotic expansions of the distribution function of the normalized maximum value of the mixed partial t distribution under the condition of power normed are obtained. In the second part, under the condition of linear normed and power normed, the higher order asymptotic expansions of the distribution function are obtained. The higher order asymptotic expansion of the density function of the normalized maximum value of the mixed partial t distribution. Firstly, the expression of the density function of the mixed partial t distribution is obtained by using the expression of the density function of the partial partial t distribution. Secondly, the expression of the density function of the mixed partial t distribution is obtained. In the first part, the higher order asymptotic expansion of the distribution function of the normalized maximum value and the density function of the mixed partial t distribution are obtained under the condition of linear normed and power normed respectively. The higher order asymptotic expansion of the density function of the normalized maximum value under two normed conditions can be obtained. The third part is based on the first part. Through two examples, the distribution function of normalized maximum value and the asymptotic expansion of density function are simulated and compared with the corresponding exact values. Finally, it is shown in the form of graphs, and the difference of fitting accuracy of higher order asymptotic expansion under linear normed and power normed conditions is more intuitively reflected.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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