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 paper, asymptotic expansions of the non-null distribution of the likelihood ratio criterion for testing the equality of several one parameter exponential distributions are obtained under local alternatives, in terms of Chi-square distributions.
Abstract: In this paper asymptotic expansions of the non-null distribution of the likelihood ratio criterion for testing the equality of several one parameter exponential distributions are obtained under local alternatives. These expansions are in terms of Chi-square distributions.
1 citations
01 Jan 1995
TL;DR: Algorithms for the generation of pseudorandom numbers with normal and exponential distributions are described here, which are much faster than other exponential and normal random number generators.
Abstract: Algorithms for the generation of pseudorandom numbers with normal and exponential distributions are described here. No transcendental functions need to be evaluated; furthermore, only two uniform deviates per generation are required; no tables are used. These algorithms are much faster than other exponential and normal random number generators.
1 citations
1 citations
07 Jan 2014
TL;DR: This work proposes the mixture of Log-normal distribution with the Exponential, Gamma, Lognormal and Weibull distributions and finds that a mixture of two different distributions approximations are even more useful comparing to theixture of two same kind of distribution for the present datasets.
Abstract: Heterogeneous survival data can have two different distributions before and after a certain time because many factors affect the life of the creatures or machines. For this purpose we use a mixture of two same kind of distribution of Exponential, Gamma, Lognormal and Weibull and a mixture of different binaries of these distributions. In addition to the previous studies, we propose the mixture of Log-normal distribution with the Exponential, Gamma and Weibull distributions. Maximum likelihood estimations of parameters of the mixture distribution models are obtained by using the EM (Expectation Maximization) algorithm. The results obtained with these models are compared with the observed data. It is found that a mixture of two different distributions approximations are even more useful comparing to the mixture of two same kind of distribution for the present datasets.
1 citations
TL;DR: In this paper, a truncated version of the shrinkage estimator is proposed, in the case of discrete exponential family, based on ordered observations which improves the minimum variance unbiased estimator.
Abstract: Let X1,…Xpbe independent random variables, where each of the p distributions of the random variables belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously in the pres¬ence of extreme observations. Hudson (1978) and Tsui (1979) show that the minimum variance unbiased estimator (MVUE) of the param¬eters is inadmissible if p⩾3 under squared error loss, and esti¬mators better than MVUE are proposed. In this paper, a truncated version of the shrinkage estimator is proposed, in the case of discrete exponential family. This estimator is based on ordered observations which improves the MVUE.
1 citations