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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01 Jan 1998
TL;DR: In this article, the relation between natural exponential families and Sheffer polynomials was investigated using the Umbral calculus and a new transparent proof of Feinsilver's theorem was given.
Abstract: We use the Umbral Calculus to investigate the relation between natural exponential families and Sheffer polynomials. As a corollary, we obtain a new transparent proof of Feinsilver’s theorem which says that natural exponential families have a quadratic variance function if and only if their associated Sheffer polynomials are orthogonal.
8 citations
TL;DR: In this paper, it is shown numerically through various examples that the posterior distribution for the parameter and the induced fiducial distribution are almost equivalent, and inference procedures are given, both from the classical and the Bayesian view point.
Abstract: Lindqvist and Taraldsen (2005) introduced an interesting parametric family of distributions in the unit interval. In this note, inference procedures are given, both from the classical and the Bayesian view point. It is shown numerically through various examples that the posterior distribution for the parameter and the induced fiducial distribution are almost equivalent. The parametric family under study is a regular member of the Natural Exponential Family and so use of this fact permits induction of a unique fiducial in terms of the minimal sufficient statistic.
8 citations
TL;DR: In this article, the authors studied the so-called Kumaraswamy Exponential Pareto (KEP) distribution and discussed the structural and mathematical properties of the KEP distribution.
Abstract: In this article we study the so-called Kumaraswamy Exponential Pareto (KEP) distribution. Several lifetime distributions such as the Kumaraswamy Weibull, Kumaraswamy exponential, Kumaraswamy Rayleigh, generalized Weibull, among several others are embedded in the proposed distribution. Various structural and mathematical properties of the KEP distribution are presented. We also discuss the parameter estimation and simulation methods. Real data set is used to illustrate the importance and flexibility of the proposed model.
8 citations
TL;DR: In this article, it is shown that trust region methods for solving nonlinear least squares problems are readily adapted to maximize likelihoods based on the exponential family, and that the nice theoretical results available for the non linear least squares problem also generalize.
Abstract: Many but not all attractive properties of generalized linear models associated with the exponential family of distributions are destroyed by nonlinearity. A consequence is that ensuring the stability of a computational process for maximizing the likelihood becomes relatively more important. Here it is shown that trust region methods for solving nonlinear least squares problems are readily adapted to maximize likelihoods based on the exponential family, and that the nice theoretical results available for the nonlinear least squares problem also generalize.
8 citations
TL;DR: The well known acceptance/rejection algorithm for generating random values on a computer is specialized for distribution tails using an exponential majorizing function and a linear minorizing function, which becomes particularly efficient.
Abstract: The well known acceptance/rejection algorithm for generating random values on a computer is specialized for distribution tails. Using an exponential majorizing function and a linear minorizing function, the tail algorithm becomes particularly efficient. Specific algorithms are given for the normal, gamma, Weibull and beta distributions. While the algorithms can be used alone, it is anticipated that their major value will be to serve as components of algorithms for complete distributions.
8 citations