Topic
Natural exponential family
About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.
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TL;DR: The beta exponentiated Weibull distribution is introduced which extends recent models by Lee et al. and it is demonstrated that the density of the new distribution can be expressed as a linear combination of WeIBull densities.
Abstract: The Weibull distribution is one of the most important distributions in reliability. For the first time, we introduce the beta exponentiated Weibull distribution which extends recent models by Lee et al. [Beta-Weibull distribution: some properties and applications to censored data, J. Mod. Appl. Statist. Meth. 6 (2007), pp. 173–186] and Barreto-Souza et al. [The beta generalized exponential distribution, J. Statist. Comput. Simul. 80 (2010), pp. 159–172]. The new distribution is an important competitive model to the Weibull, exponentiated exponential, exponentiated Weibull, beta exponential and beta Weibull distributions since it contains all these models as special cases. We demonstrate that the density of the new distribution can be expressed as a linear combination of Weibull densities. We provide the moments and two closed-form expressions for the moment-generating function. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The density of...
87 citations
TL;DR: In this paper, des approximations precises and facilement calculables for les densites conditionnelles and les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques are developed.
Abstract: On developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques
87 citations
TL;DR: The authors considered procedures for combining individual probability distributions that belong to some "family" into a "group" probability distribution that belongs to the same family, and applied these results to models of reaction time in psychological experiments.
87 citations
87 citations
86 citations