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, three new characterizing theorems of exponential distribution are presented based on equidistribution of some functions of order statistics, including the median of sample of size three.
Abstract: In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.
4 citations
TL;DR: In this article, a generalized generalized Rayleigh distribution is proposed for continuous random variables with a finite mean-value, where the distribution is constructed using a generalized form of the exponential distribution introduced by Isaic-Maniu and the present author.
Abstract: In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. {\it 47} (1976), pp.\,395--412. The construction makes use of the so-called ``conservability approach'' (see Kybernetika {\it 25} (1989), pp.\,209--215) namely, if $X$ is a positive continuous random variable with a finite mean-value $E(X)$, then a new density is set to be $f_1(x) = x f(x)/E(X)$, where $f(x)$ is the probability density function of $X$. The new generalized Rayleigh variable is obtained using a generalized form of the exponential distribution introduced by Isaic-Maniu and the present author as $f(x)$.
4 citations
TL;DR: In this paper, the distribution of coherent radiation propagating in a random medium is analyzed in the framework of diagram technique and it is shown that only for small values of the argument the distribution function is a simple exponential, as predicted by Rayleigh statistics.
Abstract: Statistics of coherent radiation propagating in a random medium is analyzed in the framework of diagram technique. The distribution function for radiation intensity is calculated and it is shown, that only for small values of the argument the distribution function is a simple exponential, as predicted by Rayleigh statistics. For larger values of intensity the distribution function differs drastically from the simple exponential, and the asymptotical behavior is a stretched exponential. The results obtained are confirmed by numerical simulations.
4 citations
01 Jul 1997
TL;DR: This paper proposes three kinds of models for obtaining exponential possibility distributions, namely, the upper approximation model, the lower approximation model and the integrated model to reflect the different viewpoints.
Abstract: This paper proposes three kinds of models for obtaining exponential possibility distributions, namely, the upper approximation model, the lower approximation model and the integrated model to reflect the different viewpoints. An example of the possibility distribution in a portfolio selection problem is shown.
4 citations
TL;DR: In this article, the class of natural exponential families (NEF) for which Shtarkov distributions exist and Jeffreys distributions do not has been studied and a general result which enables us to construct numerous classes of infinitely divisible NEF's for which the Shtakov distribution exists and the Jeffreys distribution does not.
4 citations