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Laplace Transform Asymptotics and Large Deviation Principles for Longest Success Runs in Bernoulli Trials
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden..
Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden..
2016 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, 747-764 p.Article in journal (Refereed) Published
Abstract [en]

The longest stretch L(n) of consecutive heads in n independent and identically distributed coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of L(n) and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of L(n) near its nominal value log(1/p) n and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L(n).

Place, publisher, year, edition, pages
2016. Vol. 53, no 3, 747-764 p.
Keyword [en]
Large deviation principle, rate function, Fenchel-Legendre transform, Laplace transform, moment generating function, run, longest run, Bernoulli trial, confidence interval
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-308783DOI: 10.1017/jpr.2016.38ISI: 000386349900008OAI: oai:DiVA.org:uu-308783DiVA: diva2:1053223
Funder
Swedish Research Council
Available from: 2016-12-08 Created: 2016-11-30 Last updated: 2016-12-08Bibliographically approved

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