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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a measure of the algebraic independence of the values of the exponential function and certain other functions is established, and a theorem is proved on the number of algebraically independent quantities among a series of values of a given exponential function.
Abstract: Estimates are established for a measure of the algebraic independence of the values of the exponential function and certain other functions, and a theorem is proved on the number of algebraically independent quantities among a series of values of the exponential function.Bibliography: 11 titles.

20 citations

Journal ArticleDOI
TL;DR: In this paper, the behavior of a sequence of independent identically distributed random variables with respect to a random threshold is investigated, and three statistics connected with exceeding the threshold are introduced, their exact and asymptotic distributions are derived.
Abstract: Behaviour of a sequence of independent identically distributed random variables with respect to a random threshold is investigated. Three statistics connected with exceeding the threshold are introduced, their exact and asymptotic distributions are derived. Also distribution-free properties, leading to some common and some new discrete distributions, are considered. Identification of equidistribution of observations and the threshold are discussed. In this context relations between the exponential and gamma distributions are studied and a new derivation of the celebrated Laplace expansion for the standard normal distribution function is given.

20 citations

Journal ArticleDOI
01 Mar 2009
TL;DR: The authors derived recurrence relations for single and product moments of generalized order statistics (gOSs) from linear exponential distribution and characterizations of this distribution based on the conditional moments of the gOSs are given.
Abstract: In this paper, recurrence relations for single and product moments of generalized order statistics (gOSs) from linear exponential distribution (LE) are derived and characterizations of this distribution based on the conditional moments of the gOSs are given.

20 citations

Journal ArticleDOI
TL;DR: In this article, the robustness of some existing tests for the exponential distribution when some outliers are present is reviewed and some tests for outliers in the exponential case are proposed.
Abstract: In this paper the robustness of some of the existing tests for the exponential distribution when some outliers are present is reviewed. It is noted that the tests proposed by Epstein and Sobel [4] can be used without any major modification in the presence of outliers and a more suitable flexible test criterion is proposed for the exponential lower limit which is superior to Carlson's statistic [2] in all situations. The distribution of this statistic is derived and tables are constructed to facilitate the use of this statistic. Also some tests for outliers in the exponential case are proposed.

20 citations

Proceedings ArticleDOI
11 Feb 2016
TL;DR: In this article, a convolution of generated random variable from independent and identically exponential distribution with stabilizer constant is constructed and the characteristic function of this distribution is obtained by using Laplace-Stieltjes transform.
Abstract: It is constructed convolution of generated random variable from independent and identically exponential distribution with stabilizer constant. The characteristic function of this distribution is obtained by using Laplace-Stieltjes transform. The uniform continuity property of characteristic function from this convolution is obtained by using analytical methods as basic properties.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202262
202114
202010
20196
201823