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: In this paper, the authors introduced a new distribution, which generalizes linear failure rate distribution, and the properties of this distribution are discussed in this distribution and a real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well known distributions.
Abstract: The exponential and Rayleigh are the two most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. Unfortunately, the exponential distribution only has constant failure rate and the Rayleigh distribution has increasing failure rate. The linear failure rate distribution generalizes both these distributions which may have non increasing hazard function also. This article introduces a new distribution, which generalizes linear failure rate distribution. This distribution generalizes the well-known (1) exponential distribution, (2) linear failure rate distribution, (3) generalized exponential distribution, and (4) generalized Rayleigh distribution. The properties of this distribution are discussed in this article. The maximum likelihood estimates of the unknown parameters are obtained. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well-known ...
103 citations
Journal Article•
TL;DR: Families of probability distributions which arise naturally as parameter likelihoods in conjugate prior distributions for exponential families are identified, described and their relevance to computational issues in Bayes hierarchical models noted as mentioned in this paper.
Abstract: Families of probability distributions which arise naturally as parameter likelihoods in conjugate prior distributions for exponential families are identified, described and their relevance to computational issues in Bayes hierarchical models noted.
103 citations
TL;DR: In this paper, the problem of predicting the rth ordered observation Xr in a sample of n from an exponential distribution, based on the observed values of the first k ordered observations from the sample (k < r ≤ n), is discussed.
Abstract: The problem of predicting the rth ordered observation Xr in a sample of n from an exponential distribution, based on the observed values of the first k ordered observations from the sample (k < r ≤ n), is discussed. It is shown how to find an interval estimate for Xr , and the result is used to predict the remaining elapsed time in certain life test experiments involving items whose life times follow an exponential distribution.
103 citations
102 citations
TL;DR: A new class of bivariate distributions is presented in this paper, which is based on a latent random variable with exponential distribution, and the model introduced here is of Marshall-Olkin type.
101 citations