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 paper, the authors introduce a method which allows perfect sampling from random graph models in exponential family form ("exponential family random graph" models), using a variant of Coupling From The Past.
Abstract: Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form ("exponential family random graph" models), using a variant of Coupling From The Past. We illustrate the use of the method via an application to the Markov graphs, a family that has been the subject of considerable research. We also show how the method can be applied to a variant of the biased net models, which are not exponentially parameterized.
13 citations
TL;DR: In this paper, the authors construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values, based on characterizations presented in [2] and [3].
Abstract: We construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values. Our approach is based on characterizations presented in [2]–[4], [5], [9].
13 citations
TL;DR: In this article, a flexible 3-parameter generalization of the exponential distribution is introduced based on the binomial exponential 2 (BE2) distribution, which exhibits decreasing, increasing and bathtub-shaped hazard rates, so it turns out to be quite flexible for analyzing nonnegative real life data.
Abstract: Developing statistical methods to model hydrologic events is always interesting for both statisticians and hydrologists, because of its importance in hydraulic structures design and water resource planning. Because of this, a flexible 3-parameter generalization of the exponential distribution is introduced based on the binomial exponential 2 (BE2) distribution [2]. The proposed distribution involving the exponential, gamma and BE2 distributions as submodels; and it exhibits decreasing, increasing and bathtub-shaped hazard rates, so it turns out to be quite flexible for analyzing non-negative real life data. Some statistical properties, parameters estimation and information matrix of the distribution are investigated. The proposed distribution, Gumbel, generalized Logistic and other distributions are utilized to model and fit two hydrologic data sets. The distribution is shown to be more appropriate to the data than the compared distributions using the selection criteria: average scaled absolute er...
13 citations
13 citations
TL;DR: In this paper, the moment generating function of a conjugate exponential family distribution for the canonical parameter can be conveniently written in terms of the corresponding normalising constant for the conjugates densities.
Abstract: SUMMARY For exponential families, the moment generating function of a conjugate exponential family distribution for the canonical parameter can be conveniently written in terms of the corresponding normalising constant for the conjugate densities. This result can be used to find the moments of the canonical parameter and certain functions thereof. This is illustrated for the class of natural exponential families having a simple quadratic variance function. Two applications are outlined. The first is concerned with the analysis of dynamic generalised linear models, as put forward by West, Harrison & Migon (1985). The second refers to the calculations of the expected logarithmic divergence for exponential families under a conjugate distribution.
13 citations