Journal ArticleDOI
Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire
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This article is published in Annals of Mathematics.The article was published on 1943-07-01. It has received 2037 citations till now.read more
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Probabilistic modeling of quasibrittle fracture and size effect
TL;DR: In this article, the authors describe the recent efforts to combin eth eclassica lWeibul ltheor yo fstatistica lsiz eeffec tdu et al. with the recently developed energetic theory, and also survey various related problems such as the probability tail structure of the stochastic finite element methods, the random scatter in fracture testing, the role of fractal nature of cracks, the reliability provisions of design codes, and the lessons from past structural catastrophes.
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A form of regular variation and its application to the domain of attraction of the double exponential distribution
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Handbook of Exponential and Related Distributions for Engineers and Scientists
Nabendu Pal,Chun Jin,Wooi K. Lim +2 more
TL;DR: In this article, the authors present a model for estimating the good fit of a test set for exponential distribution with respect to a set of parameters using Monte-Carlo simulation and Bayes rules.
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Equivalence classes of regularly varying functions
TL;DR: In this article, equivalence classes of regularly varying functions (in the extended sense) are studied, which is relevant to the problems mentioned above. But this method involves an extended theory of regular varying functions.
Journal ArticleDOI
Right tail expansion of Tracy-Widom beta laws
Gaëtan Borot,Céline Nadal +1 more
TL;DR: In this paper, a physical derivation of the all order asymptotic expansion of the right tail Tracy-Widom beta laws, for all positive beta, by studying the double scaling limit was given.