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September 2016 Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials
Takis Konstantopoulos, Zhenxia Liu, Xiangfeng Yang
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J. Appl. Probab. 53(3): 747-764 (September 2016).

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∕pn and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L(n).

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Takis Konstantopoulos. Zhenxia Liu. Xiangfeng Yang. "Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials." J. Appl. Probab. 53 (3) 747 - 764, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60030
MathSciNet: MR3570092

Subjects:
Primary: 60F10
Secondary: 44A10 , 60G50 , 60G70

Keywords: Bernoulli trial , Confidence interval , Fenchel–Legendre transform , Laplace transform , large deviation principle , longest run , moment generating function , Rate function , Run

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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