On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials

Kiyoshi Inoue () and Sigeo Aki

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 7, 895-920

Abstract: In this article, we study sooner/later waiting time problems for simple patterns in a sequence of bivariate trials. The double generating functions of the sooner/later waiting times for the simple patterns are expressed in terms of the double generating functions of the numbers of occurrences of the simple patterns. Effective computational tools are developed for the evaluation of the waiting time distributions along with some examples. The results presented here provide perspectives on the waiting time problems arising from bivariate trials and extend a framework for studying the exact distributions of patterns. Finally, some examples are given in order to illustrate how our theoretical results are employed for the investigation of the waiting time problems for simple patterns. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Sooner and later waiting times; Probability generating function; Pattern; Double generating function; Multiple players problem; Polya urn model; Primary 60E05; Secondary 60J10 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:77:y:2014:i:7:p:895-920

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DOI: 10.1007/s00184-013-0478-0

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