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 2014
TL;DR: In this article, the authors estimate the parameters of weighted exponential model, obtained by using the idea of Azzalini, which results in a new class of WE distributions, which have the probability density function (PDF) whose shape is very close to the shape of the PDF of weibull, gamma or generalized exponential distributions.
Abstract: There are many ways to introduce a shape parameter to an exponential distribution. The different methods may results in variety of weighted exponential (WE) distribution. In this article, we try to estimate the parameters of weighted exponential model, obtained by using the idea of Azzalini, which results in a new class of WE distributions. This new WE model has the probability density function (PDF) whose shape is very close to the shape of the PDF of weibull, gamma or generalized exponential distributions. This model can be used as an alternative to any of these distributions. The maximum likelihood and moment of the estimator are derived for samples from the WE distribution. These estimators are compared empirically when all the parameters are unknown, their bias and determinants are investigated with help of numerical technique, and have shown that moment estimator is unbiased.
4 citations
TL;DR: In this paper , a new one-parameter discrete length-biased exponential distribution called the discrete moment exponential (DMEx) distribution is introduced using the survival discretizing approach.
4 citations
TL;DR: In this article, the problem of estimating an unknown distribution parameter of a particular exponential family of distributions is considered under LINEX loss function for estimation error and a cost c > 0 for each of an i.i.d. sequence of potential observations X1, X2,...
Abstract: The problem of sequentially estimating an unknown distribution parameter of a particular exponential family of distributions is considered under LINEX loss function for estimation error and a cost c > 0 for each of an i.i.d. sequence of potential observations X1, X2, . . . A Bayesian approach is adopted and conjugate prior distributions are assumed. Asymptotically pointwise optimal and asymptotically optimal procedures are derived.
4 citations
Journal Article•
TL;DR: In this article, a characterization of the multivariate Marshall-Olkin exponential distribution is derived and the maximum likelihood estimators and the moment estimators for parameters of the MLE distribution are obtained.
Abstract: A characterization of the multivariate Marshall-Olkin exponential distribution is derived. Using this characterization, the maximum likelihood estimators and the moment estimators for parameters of the multivariate Marshall-Olkin exponential distribution are obtained.
4 citations
TL;DR: In this paper, a simple information matrix misspecification test for exponential distributions that can be applied in duration models is presented. But the test performance is not evaluated using Monte Carlo simulation experiments.
Abstract: We construct a simple information matrix misspecification test for exponential distributions that can be applied in duration models. We evaluate the test performance using Monte Carlo simulation experiments. We found good empirical size properties and good power against Weibull and Gamma distributions.
4 citations