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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.


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Journal ArticleDOI
15 Aug 2012
TL;DR: In this article, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics, and specific distributions are considered as a particular case of the general class of distributions.
Abstract: In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

2 citations

Journal ArticleDOI
TL;DR: This article studies the moment-based test procedure for a mixture distribution for the Natural exponential family with quadratic variance functions (NEF-QVF) family proposed by Ning et al. (2009b) in the small sample size scenario and derives the approximation for the null distribution of the test statistic by the Edgeworth expansion.
Abstract: In this article, we study the moment-based test procedure for a mixture distribution for the Natural exponential family with quadratic variance functions (NEF-QVF) family proposed by Ning et al. (2009b) in the small sample size scenario. We derive the approximation for the null distribution of the test statistic by the Edgeworth expansion. The simulations are conducted for a binomial mixture distribution, which includes the situation corresponding to the detection of the linkage in the genetic analysis, with different sample sizes and family sizes at various significance levels. The simulation results show that our test performs reasonably well. We also apply the proposed method to the real clinical data to verify the significant difference between two drug treatments. The critical values associated with a binomial mixture distribution are also provided.

2 citations

Journal ArticleDOI
TL;DR: In this article, a unified approach for computing nonequal tail optimal confidence intervals (CIs) for the scale parameter of the exponential family of distributions is presented, where all equations are reduced into a system of two equations that can be solved via a straightforward algorithm.
Abstract: This article presents a unified approach for computing nonequal tail optimal confidence intervals (CIs) for the scale parameter of the exponential family of distributions. We prove that there exists a pivotal quantity, as a function of a complete sufficient statistic, with a chi-square distribution. Using the similarity between equations of shortest, unbiased, and highest density CIs, all equations are reduced into a system of two equations that can be solved via a straightforward algorithm.

2 citations

Journal ArticleDOI
TL;DR: In this article, a unified Bayesian approach for comparing scale parameters in an exponential family, assuming other parameters such as location or shape are known, is proposed, and the results are illustrated in the comparison of scales of two normals and two Weibull densities.
Abstract: This article considers a unified Bayesian approach for comparing scale parameters in an exponential family, assuming other parameters such as location or shape, are known. Particular cases include the normal, gamma, Weibull, exponential, Poisson, and binomial distributions. Convenient conjugate priors are found in joint distribution conditionally specified. Hyperparameter elicitation techniques are discussed. The results are illustrated in the comparison of scales of two normals and two Weibull densities.

2 citations


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