LAPLACE TRANSFORM ASYMPTOTICS AND LARGE DEVIATION PRINCIPLES FOR LONGEST SUCCESS RUNS IN BERNOULLI TRIALS
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
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
CAMBRIDGE UNIV PRESS , 2016. Vol. 53, no 3, 747-764 p.
Large deviation principle; rate function; Fenchel-Legendre transform; Laplace transform; moment generating function; run; longest run; Bernoulli trial; confidence interval
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:liu:diva-132686DOI: 10.1017/jpr.2016.38ISI: 000386349900008OAI: oai:DiVA.org:liu-132686DiVA: diva2:1048194
Funding Agencies|Swedish Research Council [2013-4688]2016-11-212016-11-182016-11-21