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 article, a matrix formula for second-order covariances of maximum likelihood estimators in exponential family nonlinear models was given, thus generalizing the result of Cordeiro (2004) valid for generalized linear models with known dispersion parameter.
Abstract: This article gives a matrix formula for second-order covariances of maximum likelihood estimators in exponential family nonlinear models, thus generalizing the result of Cordeiro (2004) valid for generalized linear models with known dispersion parameter. Some simulations show that the second-order covariances for exponential family nonlinear models can be quite pronounced in small to moderate sample sizes.
5 citations
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TL;DR: In this paper, the asymptotic distribution of the log-likelihood ratio is used to determine approximate confidence bounds for the reliability function of any coherent system when each component has an exponential life with unknown failure rate and component performance data are provided.
Abstract: The asymptotic distribution of the log-likelihood ratio is shown to provide a method of determining approximate confidence bounds for the reliability function of any coherent system when each component has an exponential life with unknown failure rate and component performance data are provided in the form: number of failures (minimum of one) and total operating time. Thus the method applies under all general types of censoring. This extends the results of the authors, Ann. Math. Statist. (1968), on confidence limits for coherent structures with binomial data on the component's reliability. Methods similar to those previously utilized are combined with some special properties of the exponential distribution to obtain the results.
5 citations
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31 Jan 2012
TL;DR: In this article, the authors derived approximate maximum likelihood estimators of two parameters in a weighted exponential distribution, and derived the density function for the ratio Y of the maximum likelihood estimate.
Abstract: We derive approximate maximum likelihood estimators of two parameters in a weighted exponential distribution, and derive the density function for the ratio Y
5 citations
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TL;DR: In this article, a bivariate distribution supported on the first quadrant with exponential, and heavy tailed Mittag-Leffer, marginal distributions is introduced, which is a rather special case that does not follow their general theory.
5 citations
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01 Jan 2009TL;DR: The vast majority of the bivariate exponential distributions arise in the reliability context one way or another as mentioned in this paper, and most of them arise from the failure of an item or death of a living organism.
Abstract: The vast majority of the bivariate exponential distributions arise in the reliability context one way or another. When we talk of reliability, we have in mind the failure of an item or death of a living organism. We especially think of time elapsing between the equipment being put into service and its failure. In the bivariate or multivariate context, we are concerned with dependencies between two failure times, such as those of two components of an electrical, mechanical, or biological system.
5 citations