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On Occurrences of F-S Strings in Linearly and Circularly Ordered Binary Sequences

Part of: Limit theorems Stochastic processes Distribution theory - Probability Distribution theory Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Frosso S. Makri
Frosso S. Makri*
Affiliation:
University of Patras
*
∗Postal address: Department of Mathematics, University of Patras, 26500 Patras, Greece. Email address: [email protected]
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Abstract

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Consider a sequence of exchangeable or independent binary trials ordered on a line or on a circle. The statistics denoting the number of times an F-S string of length (at least) k1 + k2, that is, (at least) k1 failures followed by (at least) k2 successes in n such trials, are studied. The associated waiting time for the rth occurrence of an F-S string of length (at least) k1 + k2 in linearly ordered trials is also examined. Exact formulae, lower/upper bounds and approximations are derived for their distributions. Mean values and variances of the number of occurrences of F-S strings are given in exact formulae too. Particular exchangeable and independent sequences of binary random variables, used in applied research, combined with numerical examples clarify further the theoretical results.

Keywords

Distribution of order (k1, k2)linear and circular binary sequencesexchangeable trialPoisson trialurn modelrecordsruns

MSC classification

Secondary: 60E05: Distributions 62E15: Exact distribution theory 60C05: Combinatorial probability 60G09: Exchangeability 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 157 - 178
Copyright
Copyright © Applied Probability Trust 2010 

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