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: Some compound normal distributions are obtained by ascribing to the normal mean a distribution closely related to the exponential distribution as discussed by the authors, which can cope with skewed and long-tailed data It has a location parameter which can be considered as a function of several covariates and a new set of parameters, making it possible to tackle regression problems.
Abstract: Some compound normal distributions are obtained by ascribing to the normal mean a distribution closely related to the exponential distribution The family of distribution functions found in this way can cope with skewed and long-tailed data It has a location parameter which can be considered as a function of several covariates and a new set of parameters, making it possible to tackle regression problems Maximum likelihood estimates of the parameters are obtained iteratively The first four moments of the distribution, the maximum likelihood equations and three examples of application are given
5 citations
TL;DR: In this paper, a simple data-analytic method is suggested for modelling situations in which two processes are effective on different but overlapping domains, which is used to describe a two-tendency model with exponential tails.
5 citations
TL;DR: In this paper, an asymptotic expansion of the distribution of the statistic for testing the equality of p two-parameter exponential distributions is obtained upto the order n −4 with the second term of the order N −3 where n is the size of the sample drawn from the i th exponential population.
5 citations
TL;DR: where the integral is to be interpreted as the Cauchy principal value and the sign represents the natural extension of the function El(z) ~ f~ e-$.
Abstract: where the integral is to be interpreted as the Cauchy principal value. Except for the sign, it represents the natural extension of the function El(z) ~ f~ e-$
5 citations
TL;DR: In this article, the authors derive explicit expansions for the moments of beta generalized distributions from power series expansion for the quantile functions of the baseline distributions, and apply their formula to the beta normal, beta Student t, beta gamma and beta beta generalized distribution.
Abstract: In this article, we derive explicit expansions for the moments of beta generalized distributions from power series expansions for the quantile functions of the baseline distributions. We apply our formula to the beta normal, beta Student t, beta gamma and beta beta generalized distributions. We propose a simple way to express the quantile function of any beta generalized distribution as a power series expansion with known coefficients.
5 citations