二阶次指数分布卷积与卷积根的封闭性  

Closure properties of convolution and convolution roots of second-order subexponential distribution

作　　者：陆爻 LU Yao(School of Big Data and Statistics,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学大数据与统计学院,合肥230601

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第4期460-464,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：安徽省高等学校自然科学研究基金资助项目(KJ2021A0060).

摘　　要：次指数分布作为一类重要的重尾分布,由于其能刻画大额理赔,在金融与精算领域有着广泛的应用.随着风险模型研究的进一步深入,2008年二阶次指数分布被首次提出,相对于一阶次指数分布,其渐近表达式更加精确,因而有关二阶次指数分布的研究近年来受到广泛关注.对于二阶次指数分布卷积与卷积根封闭性问题,给出了二阶次指数分布在成比例等价下关于二阶次指数分布族封闭,进而得到二阶次指数分布具有卷积封闭性,得到了二阶次指数分布关于卷积根封闭性的结论,拓展了二阶次指数分布的研究成果,对未来相关研究具有重要的理论意义.As an important heavy tail distribution,subexponential distribution was widely used in finance and actuarial fields because of its ability to describe large claims.With the further development of risk model research,the second-order subexponential distribution was firstly proposed in 2008.Compared with the first-order subexponential distribution,its asymptotic expression was more accurate,so the research on the second-order subexponential distribution had attracted extensive attention in recent years.In this paper,the closure of the convolution and the convolution roots of second-order subexponential distribution were considered.First,the closure of second-order subexponential distribution on the family of second-order subexponential distribution under proportional equivalence was given,and then the convolution closure of second-order subexponential distribution was obtained.Finally,the conclusion about the closure of convolution roots was obtained.This paper expanded the research results of second-order subexponential distribution,which had important theoretical significance for future related research.

关 键 词：二阶次指数分布 卷积 卷积根 封闭性 重尾分布 精算研究 

分 类 号：O211.3[理学—概率论与数理统计]