On discrete Gibbs measure approximation to runs

被引：5

作者：

Kumar, A. N. ^{[1
]}

Upadhye, N. S. ^{[1
]}

机构：

[1] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2022年 / 51卷 / 05期

关键词：

Runs; discrete Gibbs measure; perturbations; probability generating function; Stein operator; Stein's method; Primary; Secondary; POISSON APPROXIMATION; FIXED LENGTH; SUCCESS RUNS; DISTRIBUTIONS; (K(1);

D O I：

10.1080/03610926.2020.1765256

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：

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli trials are derived via Stein's method. The bounds obtained are new and their importance is demonstrated through an interesting application.

引用

页码：1488 / 1513

页数：26

共 35 条

[1] ON DISCRETE-DISTRIBUTIONS OF ORDER-K [J].

AKI, S ;

KUBOKI, H ;

HIRANO, K .

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1984, 36 (03) :431-440

[2]

Aki S., 1997, Advances in combinatorial methods and applications to probability and statistics, P385, DOI [10.1007/978-1-4612-4140-922, DOI 10.1007/978-1-4612-4140-922]

[3] Distributions of numbers of success runs of fixed length in Markov dependent trials [J].

Antzoulakos, DL ;

Chadjiconstantinidis, S .

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2001, 53 (03) :599-619

[4]

Antzoulakos DL., 2003, MATH STAT METHODS RE, P141, DOI [10.1142/9789812795250_0010, DOI 10.1142/9789812795250_0010]

[5] Start-up demonstration tests: models, methods and applications, with some unifications [J].

Balakrishnan, N. ;

Koutras, M. V. ;

Milienos, F. S. .

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, 2014, 30 (04) :373-413

[6]

Balakrishnan N, 1999, STAT IND TECHNOL, P251

[7]

Balakrishnan N, 2002, Runs and Scans with Applications

[8]

Barbour A. D., 2014, ARXIV14111179

[9]

Barbour A.D., 2007, ALEA-LAT AM J PROBAB, V3, P31

[10] COMPOUND POISSON APPROXIMATION FOR NONNEGATIVE RANDOM-VARIABLES VIA STEIN METHOD [J].

BARBOUR, AD ;

CHEN, LHY ;

LOH, WL .

ANNALS OF PROBABILITY, 1992, 20 (04) :1843-1866

← 1 2 3 4 →