On sum of 0-1 random variables. I. Univariate case
type: Item
instance of: scholarly article
title: On sum of 0-1 random variables. I. Univariate case
zbMATH Open document ID: 0619.60015
DOI: 10.1007/BF02491451
author: Akimichi Takemura
author: Kei Takeuchi
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: This article deals with the exact distribution of \(S_ n=X_ 1+...+X_ n\) where \(X_ 1,...,X_ n\) are 0-1 random variables. Independence or exchangeability is not assumed. The distribution of \(S_ n\) is studied by evaluating the factorial moments and then using the fact that the factorial moments determine the distribution. A binomial approximation of the distribution of \(S_ n\) is obtained through orthogonal expansions in terms of orthogonal polynomials in the category of Krawtchouk polynomials. Poisson and normal type approximations are also obtained by exploiting the factorial moments.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 4005227
zbMATH Keywords: orthogonal expansions
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: factorial moments
reviewed by: Arakaparampil M. Mathai
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4005227