On the number of appearances of a word in a sequence of i. i. d. trials
type: Item
instance of: scholarly article
title: On the number of appearances of a word in a sequence of i. i. d. trials
zbMATH Open document ID: 0949.60014
DOI: 10.1023/A:1010042628865
author: Ourania Chryssaphinou
author: Eutichia Vaggelatou
author: Stavros Papastavridis
published in: Methodology and Computing in Applied Probability
publication date: 2000-12-03T00:00:00Z
review text: Let \(X_1,\dots,X_n\) be a sequence of independent and identically distributed random variables taking values in a finite alphabet \({\mathcal A}\), whose common distribution is not necessarily uniform. For a given word \(W\) composed of letters of \({\mathcal A}\), bounds are given for the accuracy in total variation of a Poisson approximation to the number \(R(W)\) of appearances of \(W\) as a renewal, and for a compound Poisson approximation to the total number \(N(W)\) of appearances of \(W\). The main tool in the proof is the Stein-Chen method. A number of numerical examples are computed.
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 1394696
reviewed by: A. D. Barbour
MaRDI profile type: Publication
full work available at URL: a:1010042628865
OpenAlex ID: W42698946
description: scientific article; zbMATH DE number 1394696