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 article, the authors present two types of symmetric scale mixture probability distributions which include the normal, Student t, Pearson Type VII, variance gamma, exponential power, uniform power and generalized t distributions.
Abstract: Summary
This paper presents two types of symmetric scale mixture probability distributions which include the normal, Student t, Pearson Type VII, variance gamma, exponential power, uniform power and generalized t (GT) distributions. Expressing a symmetric distribution into a scale mixture form enables efficient Bayesian Markov chain Monte Carlo (MCMC) algorithms in the implementation of complicated statistical models. Moreover, the mixing parameters, a by-product of the scale mixture representation, can be used to identify possible outliers. This paper also proposes a uniform scale mixture representation for the GT density, and demonstrates how this density representation alleviates the computational burden of the Gibbs sampler.
58 citations
TL;DR: In this article, a method for modeling two-dimensional and three-dimensional particle size distributions using the Weibull distribution function was proposed, which can also be used to compute the corresponding relative frequency distributions.
57 citations
TL;DR: For a given number n of different exponential distributions, the class investigated in this paper is an (n - 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions.
Abstract: Linear combinations of exponential distribution functions are considered, and the class of distribution functions so obtainable is investigated. Convex combinations correspond to hyperexponential distributions, while non-convex combinations yield, among other, generalized Erlang distributions obtainable as sums of independent exponential random variables with different parameters. For a given number n of different exponential distributions, the class investigated is an (n - 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions. The geometric aspect of this subset is revealed, together with the location of hyperexponential and generalized Erlang distributions.
57 citations
57 citations
TL;DR: In this paper, the maximum likelihood estimation problem for the singly truncated normal family of distributions was studied and necessary and sufficient conditions in terms of the coefficient of variation were provided to obtain a solution to the likelihood equations.
Abstract: This paper is concerned with the maximum likelihood estimation problem for the singly truncated normal family of distributions. Necessary and suficient conditions, in terms of the coefficient of variation, are provided in order to obtain a solution to the likelihood equations. Furthermore, the maximum likelihood estimator is obtained as a limit case when the likelihood equation has no solution.
56 citations