两个Sarmanov相依随机变量关于S(γ)族的乘积封闭性  

Product Closure Property of Two Sarmanov Dependent Random Variables about Convolution Equivalence Distributions

作　　者：杨月丽 高宇 YANG Yueli;GAO Yu(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《安庆师范大学学报（自然科学版）》2022年第3期47-52,共6页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学基金(1808085MA16)。

摘　　要：卷积等价分布族S(γ)是应用概率论中一类重要的分布族,S(γ)族关于乘积运算的封闭性是一个基本的理论问题。假设随机向量(X,Y)服从二维Sarmanov分布,且X属于S(γ)族,在一定条件下,利用概率极限理论以及独立情形下的结果,得到了XY属于S(γ)族的若干充分条件,并推广了已有结果。结论可应用于分支过程、排队论和风险理论等相关领域。The convolution equivalence distribution class S(γ)is an important distribution class in applied probability.It is a fundamental theoretical problem for studying the product closure property about the class S(γ).This paper assumes that the random vector(X,Y)follows a bivariate Sarmanov distributions and the random variable X belongs to the class S(γ).Under certain conditions,by using probability limit theory and some results of the independent case,some sufficient condi-tions for XY belonging to S(γ)are derived,which extends the existing results.The conclusions can be applied to related fields such as branching process,queuing theory,and risk theory.

关 键 词：S(γ)族 Sarmanov分布 封闭性 独立 风险理论 

分 类 号：O211.4[理学—概率论与数理统计]