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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.


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Journal ArticleDOI
01 Dec 1970-Metrika
TL;DR: In this article, the authors use a desk calculator to calculate the probability of the rejection of suspected observed outliers in a set of beta functions, which can be expressed in terms of a finite series of Beta functions.
Abstract: Likes obtains the distributions ofDixon’s statistics for an exponential population and tabulates upper 100α% points (α=0.1, 0.05, 0.01) of some of these distributions. The distribution of these statistics can be expressed in terms of finite series of beta functions and hence the probabilities of the rejection of suspected observed outliers may be easily calculated on a desk calculator. Thus we may avoid the difficult task of tabulating 100α% values of these statistics.

26 citations

Journal ArticleDOI
01 Jun 1994-Test
TL;DR: Shanbhag's clever method for finding the Jorgensen set of the family of Wishart distributions on symmetric matrices is extended here to Wishart distribution on asymmetric cones, such as Hermitian matrices on complex numbers or quaternions.
Abstract: Shanbhag’s clever method for finding the Jorgensen set of the family of Wishart distributions on symmetric matrices is extended here to Wishart distributions on symmetric cones, such as Hermitian matrices on complex numbers or quaternions. The idea is also extended to various other multivariate distributions, including the natural exponential family associated with the set of normal distributions onR with unknown mean and variance.

26 citations

Journal ArticleDOI
TL;DR: In this article, the tail asymptotics of certain mixtures of Poisson distributions show that they are Paretian, their tail index being one of the parameters deening these laws.
Abstract: Tail asymptotics of certain mixtures of Poisson distributions show that they are Paretian, their tail index being one of the parameters deening these laws. Estimators similar to those proposed by Press 15] for continuous stable laws are then used for the estimation of the parameters of such laws and asymptotic properties are proved. Inference is based on the empirical probability generating function. As special cases the discrete stable distribution, the discrete Linnik distribution, and the Sibuya distribution are examined.

26 citations

Journal ArticleDOI
TL;DR: In this paper, a spectrum of related characterizations of the exponential distribution are identified and verified, motivated by the observation that for a sample of size two from an exponential distribution, the largest order statistic is distributed as a convolution of two independent exponential random variables with distributions differing only in their intensity or rate parameter.

26 citations

Journal ArticleDOI
TL;DR: In this article, the moments of a NBWUE family of life distributions were derived for weak and moderate convergence conditions, and the equivalence of weak convergence and moment convergence was established under mild conditions.

26 citations


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