Infinitely Divisible Approximations for Sums of m-Dependent Random Variables

被引：1
|
作者：
Vellaisamy, P. [1 ]
Cekanavicius, V. [2 ]
机构：
[1] Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, India
[2] Vilnius Univ, Dept Math & Informat, Naugarduko 24, LT-03225 Vilnius, Lithuania
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2018年 / 31卷 / 04期
关键词：
Compound Poisson distribution; Uniform Kolmogorov theorem; m-dependent variables; Total variation norm; Local norm;
D O I：
10.1007/s10959-017-0774-0
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Assuming conditions on factorial cumulants, we estimate the closeness of distribution of a sum of nonnegative integer-valued m-dependent random variables to the class of all infinitely divisible laws. The accuracy of approximation is measured in total variation and local metrics. Our results are exemplified by an analogue of the first uniform Kolmogorov theorem for the statistic of (k(1), k(2)) events.
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页码：2432 / 2445
页数：14
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