Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials
- 1 September 2016
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 53 (3) , 747-764
- https://doi.org/10.1017/jpr.2016.38
Abstract
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 log1∕p n and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L(n).Keywords
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This publication has 13 references indexed in Scilit:
- Runs in coin tossing: a general approach for deriving distributions for functionalsJournal of Applied Probability, 2015
- Some results associated with the longest run in a strongly ergodic Markov chainActa Mathematica Sinica, English Series, 2013
- Large Deviation Behavior for the Longest Head Run in an IID Bernoulli SequenceJournal of Theoretical Probability, 2013
- Large Deviations Techniques and ApplicationsPublished by Springer Nature ,2010
- On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trialsJournal of Applied Probability, 2003
- Longest runs in a sequence ofm-dependent random variablesProbability Theory and Related Fields, 1992
- The Longest Run of HeadsThe College Mathematics Journal, 1990
- THE USE OF CONFIDENCE OR FIDUCIAL LIMITS ILLUSTRATED IN THE CASE OF THE BINOMIALBiometrika, 1934
- Probable Inference, the Law of Succession, and Statistical InferenceJournal of the American Statistical Association, 1927
- Das Problem der Iterationen,ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1921