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: The Kummer beta generalized family as mentioned in this paper is a family of distributions that extends the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions.
Abstract: Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes.We define
and study a new class of distributions called the Kummer beta generalized family to extend the
normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions.
Some special models are discussed. The ordinary moments of any distribution in the new family
can be expressed as linear functions of probability weighted moments of the baseline distribution.
We examine the asymptotic distributions of the extreme values. We derive the density function
of the order statistics, mean absolute deviations and entropies. We use maximum likelihood
estimation to fit the distributions in the new class and illustrate its potentiality with an application
to a real data set.
49 citations
TL;DR: In this article, the exact distributions of the MLEs of a two-parameter exponential distribution when the data are Type-I progressively hybrid censored are derived. But their results are not applicable to the case of hybrid censored data.
49 citations
TL;DR: In this paper, it was shown using the method of steepest descents that besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can also be derived.
Abstract: Starting from a microcanonical basis with the principle of equal a priori probability, it is shown using the method of steepest descents that besides ordinary Boltzmann-Gibbs theory with the exponential distribution a theory describing systems with power-law distributions can also be derived.
48 citations
TL;DR: In this paper, a Bayesian approach to the estimation of the parameters of a two-parameter exponential distribution and the reliability function associated with it is developed using censored samples, and it is shown that under a suitable choice of the prior distribution and of the loss function they are approximately equivalent to the corresponding maximum likelihood estimates and minimum variance unbiased estimates.
Abstract: A Bayesian approach to the estimation of the parameters of a two-parameter exponential distribution and the reliability function associated with it is developed using censored samples Bayesian point estimates are obtained for these three quantities and it is shown that under a suitable choice of the prior distribution and of the loss function they are approximately equivalent to the corresponding maximum likelihood estimates (MLE) and minimum variance unbiased estimates (MVUE) Also, Bayesian probability points and confidence points are obtained for both the parameters and their approximate equivalence is brought out
48 citations
TL;DR: In this paper, an entropic measure, which is optimized by a given arbitrary distribution with the finite linear expectation value of a physical random quantity of interest, is constructed and is concave irrespective of the properties of the distribution and satisfies the H-theorem for the master equation combined with the principle of microscopic reversibility.
Abstract: An ultimate generalization of the maximum entropy principle is presented. An entropic measure, which is optimized by a given arbitrary distribution with the finite linear expectation value of a physical random quantity of interest, is constructed. It is concave irrespective of the properties of the distribution and satisfies the H-theorem for the master equation combined with the principle of microscopic reversibility. This offers a unified basis for a great variety of distributions observed in nature. As examples, the entropies associated with the stretched exponential distribution postulated by Anteneodo and Plastino (1999 J. Phys. A: Math. Gen. 32 1089) and the κ-deformed exponential distribution by Kaniadaki (2002 Phys. Rev. E 66 056125) and Naudts (2002 Physica A 316 323) are derived. To include distributions with divergent moments (e.g., the Levy stable distributions), it is necessary to modify the definition of the expectation value.
48 citations