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Counts of failure strings in certain Bernoulli sequences
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2007 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 44, no 3, 824-830 p.Article in journal (Refereed) Published
Abstract [en]

In a sequence of independent Bernoulli trials the probability for success in the kth trial is Pk k = 1, 2..... The number of strings with a given number of failures between two subsequent successes is studied. Explicit expressions for distributions and moments are obtained for the case in which Pk = a/(a + b + k - 1), a > 0, b >= 0. Also, the limit behaviour of the longest failure string in the first n trials is considered. For b = 0, the strings correspond to cycles in random permutations.

Place, publisher, year, edition, pages
2007. Vol. 44, no 3, 824-830 p.
Keyword [en]
binomial moment, Ewens sampling formula, Hoppe's urn, Poisson, distribution, Poisson-Dirichlet distribution, Polya's urn, random, permutation, record, spacing, sums of indicators
Identifiers
URN: urn:nbn:se:kth:diva-16980ISI: 000249769900018Scopus ID: 2-s2.0-35348815650OAI: oai:DiVA.org:kth-16980DiVA: diva2:335023
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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