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KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2009 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 46, no 4, 1201-1208 p.Article in journal (Refereed) Published
Abstract [en]

In an infinite sequence of independent Bernoulli trials with success probabilities p(k) = a/(a + b + k - 1) for k = 1, 2 3, ... , let N-r be the number of r >= 2 consecutive successes. Expressions for the first two moments of N-r are derived. Asymptotics of the probability of no occurrence of r consecutive successes for large r are obtained. Using an embedding in a marked Poisson process, it is indicated how the distribution of N-r can be calculated for small r.

Place, publisher, year, edition, pages
2009. Vol. 46, no 4, 1201-1208 p.
Keyword [en]
Bernoulli trial, embedding in Poisson process, random permutation, records, runs of successes, sums of indicators, poisson processes, number, strings, counts
URN: urn:nbn:se:kth:diva-19154ISI: 000273995700019ScopusID: 2-s2.0-76449108623OAI: diva2:337201
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-02-21Bibliographically approved

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