ON CONSECUTIVE RECORDS IN CERTAIN BERNOULLI SEQUENCES
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
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.
Bernoulli trial, embedding in Poisson process, random permutation, records, runs of successes, sums of indicators, poisson processes, number, strings, counts
IdentifiersURN: urn:nbn:se:kth:diva-19154ISI: 000273995700019ScopusID: 2-s2.0-76449108623OAI: oai:DiVA.org:kth-19154DiVA: diva2:337201
QC 201005252010-08-052010-08-052011-02-21Bibliographically approved