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 give new characterizations of exponential distributions on positive semigroups and study the corresponding gamma distributions that govern semigroup products of independent and identically distributed exponential variables.
Abstract: In this paper, we give new characterizations of exponential distributions on positive semigroups and we study the corresponding gamma distributions that govern semigroup products of independent and identically distributed exponential variables. We apply these results to the positive integers under multiplication to obtain new interpretations of results on Dirichlet distributions.
5 citations
TL;DR: In this article, the concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated, and explicit formulas for common exponential families are evaluated for the generalized likelihood ratio test procedure of model selection.
Abstract: The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion.
5 citations
TL;DR: In this article, a family of multivariate distributions, which consists of scale mixtures of symmetrized Dirichlet distributions, is introduced, and the basic properties of this family such as stochastic representation, probability density functions, marginal and conditional distributions are studied.
Abstract: In this paper we introduce a family of multivariate distributions, which consists of scale mixtures of symmetrized Dirichlet distributions. This family is a symmetrization of multivariate Liouville distributions and contains the well-known spherically symmetric distributions as a special case. The basic properties of this family such as stochastic representation, probability density functions, marginal and conditional distributions and components' independence are studied. A criterion of the invariance of statistics is also given.
5 citations
TL;DR: In this article, it was shown that the maximum likelihood estimator (MLE) has asymptotic loss of information of order (n) n, as compared to constant order in regular cases.
Abstract: Fisher (1934), starting from his fundamental paper (1922), discussed estimators of the location parameter of a double exponential (two-sided exponential) distribution as a typical example of non-regular estimation. He showed that the maximum likelihood estimator (MLE), which is equal to the sample median in this case, has asymptotic loss of information of order \(\sqrt{n}\), as compared to constant order in regular cases. Let I and IT be the amounts of Fisher information in a single observation and that in a statistic T, respectively. Then the value of nI•IT as n → ∞, i.e. limn→∞ (nI — IT) is called the loss of information associated with T and its asymptotic value as n → ∞ is called the asymptotic loss of information (see, e.g. Rao (1961)).
5 citations
TL;DR: In this article, Fisher's conditionality principle is used to estimate the location parameter of an exponential distribution with known coefficient of variation, and the minimal sufficient statistic includes an a.R.
Abstract: R. A. Fisher's conditionality principle is used to estimate the location parameter of an exponential distribution with known coefficient of variation. The minimal sufficient statistic includes an a...
5 citations