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, it was shown that an arbitrary probability distribution can be represented in an exponential form, which implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in a grand canonical form.
Abstract: We show that an arbitrary probability distribution can be represented in an exponential form. In physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in a grand canonical form.
10 citations
TL;DR: In this article, a generalized gamma, the generalized Poisson, the inverse Gaussian distributions belonging to the class of exponential families are discussed. And the cumulative sums of the generalized gamma and the generalized poisson by the Chi-square are considered.
Abstract: This paper considers a generalization of the exponential type distributions in the class of exponential families. A characterization and a method of generating an exponential family from a given family are given. In particular the generalized gamma, the generalized Poisson, the inverse Gaussian distributions belonging to this family are discussed. The approximations of the cumulative sums for the generalized gamma and the generalized Poisson by the Chi-square are considered. Some of the results are extended to the bivariate case.
10 citations
01 Jan 2010
TL;DR: In this paper, the Shannon entropy function and its corresponding flow curves are analyzed and compared to examples of constrained degeneration from ordered processes, including Weibull distributions and univariate and bivariate gamma distributions.
Abstract: Gamma distributions, which contain the exponential as a
special case, have a distinguished place in the representation of
near-Poisson randomness for statistical processes; typically, they represent
distributions of spacings between events or voids among objects.
Here we look at the properties of the
Shannon entropy function and calculate its corresponding flow curves, relating
them to examples of constrained degeneration from ordered processes.
We consider also univariate and bivariate gamma, as well as Weibull distributions
since these include exponential distributions.
10 citations
TL;DR: In this paper, the authors estimate probability P { X < Y } when X and Y are two independent random variables from gamma and exponential distributions, respectively, and obtain maximum likelihood estimator and its asymptotic distribution.
Abstract: : In this paper, we estimate probability P { X < Y } when X and Y are two independent random variables from gamma and exponential distribution, respectively. We obtain maximum likelihood estimator and its asymptotic distribution. We also perform a simulation study. Keywords : Reliability; gamma distribution; exponential distribution; maximum likelihood estimator; asymptotic normality. MSC2010: 62F12, 60E05.
10 citations
TL;DR: In this paper, the authors introduced Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al. They derived the shape properties of density function and hazard function.
Abstract: Nadarajah et al.(2013) introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al.(2013). The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011).
10 citations