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.

Estimating the common location parameter of exponential distributions with censored samples

Abstract: Consider the problem of estimating the common location parameter of two exponential distributions when censored samples are taken. The unique minimum variance unbiased estimator (UMVUE) is found along with an expression for its variance. The asymptotic distribution is given for a special case and a generalized Bayes property is exhibited. Extensions include the case of k > 2 populations. Also the UMVUE is found for P(Y > X) and certain reliability functions.

Vector-Space Markov Random Fields via Exponential Families

Abstract: We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VSMRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent M-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a realworld case study of over four million foods from the popular diet tracking app My Fitness Pal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.

Hierarchical baxes predictive means and variances with application to sample survey inference

Abstract: Samples are observed from k populations having means ,(i and distributed according to a natural exponential family with quadratic variance function (NEF-QVF). Assuming an exchangeable two-stage prior, conjugate at the first stage, formulas for posterior means, variances and covariances of the μi are expressed in a unified way for all NEF-QVF models in terms of integrals over the posterior density of the two hyperparameters. This posterior density is expressed simply in terms of the normalizing function for the conjugate prior.Posterior predictive means and variances for averages of new observations are also obtained. These formulas are applied, with very little effort, to the finite population situation where the samples are independent simple random samples from the k populations, and where an exchangeable NEF-QVF superpopulation model is assumed. Posterior (predictive) means and variances for finite population totals, means and proportions are obtained. These results are illustrated with an application ...

The Marshall-Olkin-Kumarswamy-G family of distributions

Abstract: A new family of continuous distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Marshal-Olkin (Marshall and Olkin, 1997) construction. A number of known distributions are derived as particular cases. Various properties of the proposed family like formulation of the pdf as different mixture of exponentiated baseline distributions, order statistics, moments, moment generating function, Renyi entropy, quantile function and random sample generation have been investigated. Asymptotes, shapes and stochastic ordering are also investigated. The parameter estimation by methods of maximum likelihood, their large sample standard errors and confidence intervals and method of moment are also presented. Two members of the proposed family are compared with corresponding members of Kumaraswamy-Marshal-Olkin-G family (Alizadeh et al., 2015) by fitting of two real life data sets.