延拓负相依伽马分布随机变量和的尾概率上界  

The Upper Bound of Tail Probability for the Sum of Extended Negative Dependent Gamma Distribution Random Variables

作　　者：马宇波 华志强[1] 宋欢 MA Yubo;HUA Zhiqiang;SONG Huan(College of Mathematics Science,Inner Mongolia Minzu University,Tongliao 028043,China)

机构地区：[1]内蒙古民族大学数学科学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报(自然科学版)》2025年第1期17-21,共5页Journal of Inner Mongolia Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金项目(1196010102);内蒙古自治区直属高校基本科研业务费项目(GXKY23Z028);内蒙古自治区教育厅项目(JGSZ2023040);内蒙古民族大学博士科研启动基金项目(BS459,BS468);内蒙古民族大学自然科学基金项目(NMDGP17105,NMDYB18007,NMDYB2020010);内蒙古民族大学教务处课题(XJXN-KC202309)。

摘　　要：研究了延拓负相依服从不同伽马分布的不同随机变量和的尾概率上界,通过给定伽马分布的方差、概率母函数以及延拓负相依的性质,利用伽马分布的数学期望,对服从不同伽马分布的不同随机变量和的尾概率上界进行估计,得到2种不同的随机变量和的尾概率上界。对延拓负相依服从不同伽马分布的不同随机变量进行加权,利用改进的经典证明方法、伽马分布的随机变量的期望以及延拓负相依的相关性质,得到2个延拓负相依不同伽马分布不同随机变量加权和的尾概率上界。The upper bound of tail probabilities for different random variables with extended negative dependencies that follow different gamma distributions are studied.By given the variance of gamma distribution,probability generating function and the property of extended negative dependence,the tail probability upper bounds of the sum of different random variables with different gamma distributions are estimated by the mathematical expectation of gamma distribution,and the tail probability upper bounds of two different random variables are obtained.By weighting different random variables that follow different gamma distributions with extended negative dependencies,and using an improved classical proof method,the expected values of random variables in gamma distributions and the related properties of extended negative dependencies are obtained,and the tail probability upper bound of the weighted sum of two different random variables with extended negative dependencies and different gamma distributions is obtained.

关 键 词：延拓负相依 尾概率上界 加权和 

分 类 号：O211.4[理学—概率论与数理统计]