Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials
TLDR
The longest stretch $L(n)$ of consecutive heads in $n$ i.i.d. coin tosses is seen from the prism of large deviations and precise asymptotics are established for the moment generating function of L(n).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 mom ...read more
Citations
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Journal ArticleDOI
Runs and Scans With Applications
TL;DR: This text is a revision of the book by Arnold, Costillo, and Sarabia (1992), but with much more depth than the original, and comprises a lively overview of conditionally speci ed models of the conditional distribution.
Journal ArticleDOI
Degenerate Laplace transform and degenerate gamma function
TL;DR: In this paper, the degenerate Laplace transform and degenerate gamma function were investigated and some interesting formulas related to them were derived from the results of the analysis. But their properties were not discussed.
Journal ArticleDOI
A general large deviation principle for longest runs
Zhenxia Liu,Xiangfeng Yang +1 more
TL;DR: In this paper, a general large deviation principle (LDP) for the longest success run in a sequence of independent Bernoulli trails has been proved, based on the Bryc's inverse Varadhan lemma.
Journal ArticleDOI
Boundary value problems for the Dunkl Laplacian
TL;DR: In this article, the existence and uniqueness of a positive solution on the unit ball B of ℜd to the following boundary value problem were established and two cases of nonnegative perturbation φ: trivial and nontrivial.
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Large deviations for longest runs in Markov chains
Liu Zhenxia,Zhu Yurong +1 more
TL;DR: Liu et al. as discussed by the authors established a general LDP for the longest success run in a two-state Markov chain which recovers the previous result in the aforementioned paper and implemented suitable estimates of the distribution function.
References
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Book
Large Deviations Techniques and Applications
Amir Dembo,Ofer Zeitouni +1 more
TL;DR: The LDP for Abstract Empirical Measures and applications-The Finite Dimensional Case and Applications of Empirically Measures LDP are presented.
Journal ArticleDOI
The use of confidence or fiducial limits illustrated in the case of the binomial
C. J. Clopper,E. S. Pearson +1 more
Journal ArticleDOI
Probable Inference, the Law of Succession, and Statistical Inference
TL;DR: In this article, Probable Inference, the Law of Succession, and Statistical Inference are discussed, with a focus on the law of succession in probabilistic inference.