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.
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页数：11
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