Product Convolution of Generalized Subexponential Distributions

被引：4

作者：

Mikutavicius, Gustas ^{[1
]}

Siaulys, Jonas ^{[1
]}

机构：

[1] Vilnius Univ, Inst Math, Naugarduko 24, LT-03225 Vilnius, Lithuania

来源：

MATHEMATICS | 2023年 / 11卷 / 01期

关键词：

tail function; closure property; product-convolution; generalized subexponential distribution; heavy-tailed distribution; RANDOMLY WEIGHTED SUMS; RANDOM-VARIABLES; TAIL; INSURANCE; MAXIMUM;

D O I：

10.3390/math11010248

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assume that xi and eta are two independent random variables with distribution functions F-xi and F eta, respectively. The distribution of a random variable xi eta, denoted by F-xi circle times F-eta, is called the product-convolution of F-xi and F-eta. It is proved that F-xi circle times F-eta is a generalized subexponential distribution if F-xi belongs to the class of generalized subexponential distributions and eta is nonnegative and not degenerated at zero.

引用

页数：11

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