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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: The generalized transmuted-G (G-G) family as mentioned in this paper extends the G-G class with explicit expressions for the ordinary and incomplete moments, generating function, Renyi and Shannon entropies, order statistics and probability weighted moments.
Abstract: We introduce a new class of continuous distributions called the generalized transmuted-G family which extends the transmuted-G class. We provide six special models of the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of three applications to real data sets.

126 citations

Journal ArticleDOI
TL;DR: In this article, the Rao-Blackwell and Lehmann-Scheff6 theorems are used to derive the minimum variance unbiased estimates of reliability for a number of distributions that have proved useful in life testing.
Abstract: In this paper the Rao-Blackwell and Lehmann-Scheff6 theorems are used to derive the minimum variance unbiased estimates of reliability for a number of distributions that have proved useful in life testing. Estimates are also obtained for the case of censored sample in the (one- and two-parameter) exponential case. A result of Pugh comes out as a special case of the gamma and censored one-parameter exponential model and Laurent's result as a special case of the censored twoparameter exponential model.

125 citations

Journal ArticleDOI
TL;DR: A new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub is proposed, which includes as a special case the widely known exponentiated-Weibull distribution.
Abstract: We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Renyi entropies and order statistics. For the first time, we obtain the generating function of the Frechet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets. AMS Subject Classification Primary 60E05; secondary 62N05; 62F10

125 citations

Book
04 Jun 2004
TL;DR: In this paper, record statistics for exponential distribution, generalized extreme value distribution, generalized Pareto distribution, power function distribution, and geometric distribution are presented, along with some selected distributions.
Abstract: Chapter 1 Record Statistics Exponential Distribution Generalized Extreme Value Distributions Generalized Pareto Distribution Power Function Distribution Geometric Distribution Some Selected Distributions Additional Topics Complements and Problems Reference

123 citations

Journal ArticleDOI
TL;DR: In this paper, two multivariate probability distributions, namely a generalized beta and a generalized F, were derived for utility modeling, and the moments of these distributions were derived and compared to both a normal model and an unstructured model.
Abstract: Two multivariate probability distributions, namely a generalized beta and a generalizedF, that appear to be useful in utility modeling are derived. They reduce to the standard beta andF distributions, respectively, in special cases. Reproduction of distributional form is demonstrated for marginal and conditional distributions. Formulas for the moments of these distributions are given. The usefulness of these distributions in utility modeling derives from the fact that they generally do not demand increasing risk aversion as do most standard forms. An example of the use of the bivariate generalized beta distribution in utility modeling is presented. This distribution compares favorably in an example given here to both a normal model and an unstructured model.

121 citations


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