Local theorems for the Markov binomial distribution
type: Item
instance of: scholarly article
title: Local theorems for the Markov binomial distribution
zbMATH Open document ID: 1018.60025
DOI: 10.1023/A:1012802428342
author: Vydas Čekanavičius
author: M. Mikalauskas
published in: Lithuanian Mathematical Journal
publication date: 2003-05-19T00:00:00Z
review text: The Markov binomial distribution was considered by many authors [cf. \textit{R. L. Dobrushin}, Izv. Akad. Nauk SSSR, Ser. Mat. 17, 291--330 (1953; Zbl 0052.14301); \textit{J. Gani}, J. Appl. Probab., Spec. Vol. 19A, 321--326 (1982; Zbl 0488.60074); \textit{B. O. Koopman}, Proc. Natl. Acad. Sci. USA 36, 202--207 (1950; Zbl 0037.08502); \textit{R. J. Serfling}, Ann. Probab. 3, 726--731 (1975; Zbl 0321.60018); \textit{Y. H. Wang}, J. Appl. Probab. 18, 937--942 (1981; Zbl 0475.60050) and references therein]. Usually, the limit Poisson or compound Poisson laws were examined. The authors [Stochastic Processes Appl. 82, No. 2, 205--227 (1999; Zbl 0997.60073)] applied some signed compound Poisson approximations. In this paper local estimates for infinitely divisible approximations are studied. Considering the Markov binomial distribution the authors study the accuracy of infinitely divisible approximations. A local version of the Kolmogorov first uniform theorem is obtained. Possible approximations in total variation are discussed. The references contain ten bibliographical hints.
reviewed by: Ludwig Paditz
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1912581
zbMATH Keywords: Markov binomial distribution
zbMATH Keywords: Kolmogorov's theorem
zbMATH Keywords: infinitely divisible approximations
zbMATH Keywords: Markov chain
zbMATH Keywords: total variation
MaRDI profile type: Publication
full work available at URL: a:1012802428342
OpenAlex ID: W57105690
description: scientific article; zbMATH DE number 1912581