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.
Papers published on a yearly basis
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TL;DR: In this paper, a two-parameter Inverted Generalized Generalized Exponential (IGE) and a three parameter GIGE probability model were proposed as a generalization of the oneparameter Exponential distribution.
Abstract: We propose a two parameter Inverted Generalized Exponential (IGE) and a three parameter Generalized Inverted
Generalized Exponential (GIGE) probability models as generalizations of the one-parameter Exponential distribution and some other
distributions in the literature. We explore the statistical properties of the GIGE distribution and its parameters were estimated for both
censored and uncensored cases using the method of maximum likelihood estimation (MLE). An application to a real data set is also
provided to assess the flexibility of the GIGE distribution over some of its sub-models.
18 citations
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TL;DR: In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found, and group reference priors for the mean and natural parameter of the families are obtained.
18 citations
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TL;DR: In this article, an algorithm for the computation of the exponential function of real argument is presented, with no restrictions on the range of the argument or on the precision that may be demanded in the results.
Abstract: An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the results.
18 citations
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TL;DR: In this article, the integrability of empirical distribution functions was studied under various conditions on i>, [Xn], and (a] under various assumptions on [xn] and [a], where Xn is a sequence of vector valued random variables.
Abstract: If {Xn} is a sequence of vector valued random variables, {a„} a sequence of positive constants, and M = supn>l||(.Y, +. • • • + X„)/an\\\\, we examine when E($(M)) < oo under various conditions on i>, [Xn], and (a„). These integrability results easily apply to empirical distribution functions.
18 citations
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TL;DR: In this paper, a simple method for approximate conditional inference is described, which is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates.
Abstract: SUMMARY A simple method for approximate conditional inference is described The methodology is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates The approximation technique can be applied much more generally than in this particular class of models The technique depends only on the construction of certain 'projected scores' derived from higher order likelihood derivatives and their covariances and so can be used in many problems where it is relevant to control for the estimation of nuisance parameters
18 citations