Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials. (September 2016)

• Record Type: Journal Article
• Authors: Konstantopoulos, Takis; Liu, Zhenxia; Yang, Xiangfeng
• Is Part Of: Journal of applied probability. Volume 53:Number 3(2016)
• Page Start: 747
• Page End: 764
• Publication Date: 2016-09
• Subjects: Large deviation principle, -- rate function, -- Fenchel–Legendre transform, -- Laplace transform, -- moment generating function, -- run, -- longest run, -- Bernoulli trial, -- confidence interval; Primary 60F10, -- Secondary 44A10, -- 60G50, -- 60G70; 519.2
• DOI: 10.1017/jpr.2016.38
• Languages: English
• ISSNs: 0021-9002

Abstract

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 ).