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 paper, the feasibility of near ignorance classes using log-concave distributions such as the logistic and the Box and Tiao exponential power family was studied. And the main conclusion was that exponential tails are the lightest permitted in order to produce NICs with non-vacuous posterior inference, for the normal location model.
Abstract: Near ignorance classes (NIC) for the normal location model are defined in Pericchi and Walley (1991) as a proper alternative to the improper uniform prior. In this paper we study the feasibility of such classes using log-concave distributions such as the logistic and the Box and Tiao exponential power family. We use Meeden and Isaacson’s theory of posterior moments for exponential family likelihoods, as well as results for posterior distributions under log-concave priors. The main conclusion that emerges is that exponential tails are the lightest permitted in order to produce NICs with non-vacuous posterior inference, for the normal location model.
6 citations
TL;DR: In this article, three characteristic properties of a certain class of probability distributions are given based on recurrence relations between conditional moments, conditional variance and relationships between two moments of order statistics, which shed new light on some special cases obtained by the Weibull, power, Pareto, beta and Burr type XII distributions.
Abstract: Three characteristic properties of a certain class of probability distributions are given. They are based on recurrence relations between conditional moments, conditional variance and relationships between two moments of order statistics. These results shed new light on some special cases obtained by the Weibull, power, Pareto, beta and Burr type XII distributions.
6 citations
TL;DR: In this paper, the locally uniformly most powerful unbiased Lagrange multiplier test of normality of regression disturbances within the family of power exponential distributions was developed and compared in a Monte Carlo study with 6 well-known tests across 12 alternative nonnormal distributions.
Abstract: This article develops the locally uniformly most powerful unbiased Lagrange multiplier test of normality of regression disturbances within the family of power exponential distributions. The small sample power properties of the test are compared in a Monte Carlo study with 6 well-known tests across 12 alternative nonnormal distributions. In addition, the finite sample power properties for nonnormal alternatives within the power exponential family are summarized by estimating response surfaces. The results suggest that the proposed text is computationally convenient and possesses relatively attractive power properties even against alternatives outside the power exponential family.
6 citations
Book•
01 Jan 2002
6 citations
TL;DR: In this article, a characterisation of the exponential distribution is discussed based on yet another extension of the lack of memory property, motivated by a functional equation appearing in Ahsannulah.
Abstract: In this note a charactrization of the exponential distribution is discussed based on yet another extension of the lack of memory property. The result was motivated by a functional equation appearing in Ahsannulah [1], [3]
6 citations