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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, a gamma distribution with arbitrary scale parameter θ and shape parameter r < 1 can be represented as a scale mixture of exponential distributions, where θ is a Gaussian distribution.
Abstract: A gamma distribution with arbitrary scale parameter θ and shape parameter r < 1 can be represented as a scale mixture of exponential distributions

98 citations

Journal ArticleDOI
TL;DR: In this paper, conditions for strong consistency and asymptotic normality of the MLE estimator for multiparameter exponential models are given, and the conditions are less restrictive than required by general theorems in this area.
Abstract: Conditions are given for the strong consistency and asymptotic normality of the MLE (maximum likelihood estimator) for multiparameter exponential models. Because of the special structure assumed, the conditions are less restrictive than required by general theorems in this area. The technique involves certain convex functions on Euclidean spaces that arise naturally in the present context. Some examples are considered; among them, the multinomial distribution. Some convexity and continuity properties of multivariate cumulant generating functions are also discussed.

97 citations

Journal ArticleDOI
TL;DR: In this article, a procedure for finding approximate fiducial bounds on the true reliability for the two-parameter negative exponential distribution, which may be used as approximate "confidence" limits on reliability, is presented.
Abstract: We suggest herein a procedure for finding approximate fiducial bounds on the true reliability for the two parameter negative exponential distribution, which may be used as approximate “confidence” limits on reliability. These limits are simple and easy to compute. Also, they reduce to the exact confidence limits for the case of the single parameter negative exponential distribution.

97 citations

Journal ArticleDOI
TL;DR: The distribution is found to be superior to the existing sub models on being fitted to two real data sets and the non-linear equations for deriving the maximum likelihood estimators and the elements of the observed information matrix are presented.

94 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202262
202114
202010
20196
201823