有限混合费希尔分布极值密度函数的渐近性质  

Asymptotic properties of density function of extremes from mixed fisher distribution

作　　者：韦杰 曾萍 WEI Jie;ZENG Ping(School of Information Engineering,Guizhou University of Traditional Chinese Medicine,Guiyang 550025,China)

机构地区：[1]贵州中医药大学信息工程学院,贵州贵阳550025

出　　处：《安徽大学学报（自然科学版）》2024年第2期14-23,共10页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(81860695);贵州省教育科学规划课题资助项目(2015B195)。

摘　　要：设有限混合费希尔分布的分布函数由F(x)=∑_(k=1)^(r)p_(k)F_(k)(x)确定,通过对有限混合费希尔分布尾部表达式的精确展开,判断了在线性赋范和幂赋范条件下的极值分布类型分别为F∈D_(l)(Φ_(v_(1)/2))和F∈D_(p)(Φ_(1)).基于有限混合费希尔分布极值分布的渐近展开式,推导出在线性赋范和幂赋范两种不同条件下极值密度函数收敛的高阶渐近展开式,得到有限混合费希尔分布极大值密度收敛到Fréchet极值分布密度的结论.In this paper,let F(x)=∑_(k=1)^(r)p_(k)F_(k)(x) denote the distribution function of mixed Fisher distribution.By the exact expansion of its distributional tail representation,we derived the extreme value distribution types F∈D_(l)(Φ_(v_(1)/2)) and F∈D_(p)(Φ_(1))under linear and power normalization.Based on the asymptotic expansion of the extreme value distribution of mixed Fisher distribution,we deduced its the higher-order asymptotic expansion of the convergence of the extreme value density function under two different conditions of linear and power normalization,and obtained the conclusion that the maximum density of mixed Fisher distribution converges to the Fréchet extreme value distribution density.

关 键 词：有限混合 费希尔分布 渐近展开 密度函数 极值 

分 类 号：O211.4[理学—概率论与数理统计]