On large deviations for sums of discrete m-dependent random variables

被引：3

作者：

Cekanavicius, V. ^{[1
]}

Vellaisamy, P. ^{[2
]}

机构：

[1] Vilnius Univ, Dept Math & Informat, Vilnius, Lithuania

[2] Indian Inst Technol, Dept Math, Mumbai, Maharashtra, India

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2019年 / 91卷 / 08期

关键词：

Binomial distribution; large deviations; m-dependent random variables; negative binomial distribution; Poisson distribution; POISSON APPROXIMATION;

D O I：

10.1080/17442508.2019.1568438

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The ratio is investigated for three cases: (a) when is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and is Poisson rv; (b) when is a statistic of 2-runs and is negative binomial rv; and (c) when is a statistic of -events and is a binomial rv. We also consider the approximation of by the Poisson distribution with parameter depending on x.

引用

页码：1092 / 1108

页数：17

共 23 条

[1]

Aleskeviciené A, 2001, THEOR PROBAB APPL+, V46, P589, DOI 10.1137/S0040585X97979238

[2]

BARBOUR AD, 1989, SCAND J STAT, V16, P75

[3] Inequalities for the gamma function [J].

Batir, Necdet .

ARCHIV DER MATHEMATIK, 2008, 91 (06) :554-563

[4]

Cekanavicius V, 2016, UNIVERSITEXT, P1, DOI 10.1007/978-3-319-34072-2

[5]

Cekanavicius V, 2015, ALEA-LAT AM J PROBAB, V12, P765

[6]

Cekanavicius V, 2015, J THEOR PROBAB, V28, P1145, DOI 10.1007/s10959-014-0540-5

[7] SOME ASYMPTOTIC AND LARGE DEVIATION RESULTS IN POISSON APPROXIMATION [J].

CHEN, LHY ;

CHOI, KP .

ANNALS OF PROBABILITY, 1992, 20 (04) :1867-1876

[8] MODERATE DEVIATIONS IN POISSON APPROXIMATION: A FIRST ATTEMPT [J].

Chen, Louis H. Y. ;

Fang, Xiao ;

Shao, Qi-Man .

STATISTICA SINICA, 2013, 23 (04) :1523-1540

[9] LARGE DEVIATIONS BY POISSON APPROXIMATIONS [J].

DEHEUVELS, P .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1992, 32 (01) :75-88

[10]

Ghosh M., 1974, Canad. J. Statist, V2, P157

← 1 2 3 →