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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10 citations
TL;DR: In this paper, general asymptotic methods of estimating the quantile function, Q(ξ), 0<ξ<1, of location-scale families of distributions based on a few selected order statistics are considered, with applications to some nonregular distributions.
10 citations
09 Jun 2009
TL;DR: A procedure to check if a matrix exponential function of order 3 defines a ME(3) distribution or not is developed, based on the time domain analysis of the density function.
Abstract: The class of order 3 phase type distributions (PH(3)) is known to be a proper subset of the class of order 3 matrix exponential distributions (ME(3)). In this paper we investigate the relation of these two sets for what concerns their moment bounds. To this end we developed a procedure to check if a matrix exponential function of order 3 defines a ME(3) distribution or not. This procedure is based on the time domain analysis of the density function. The proposed procedure requires the numerical solution of a transcendent equation in some cases.
The presented moment bounds are based on some unproved conjectures which are verified only by numerical investigations.
10 citations
20 Aug 2015
TL;DR: In this article, the authors proposed an absolute coinuous multivariate generalized exponential distribution, which is very flexible and the joint probability density functions can take different shapes, and they provided several properties of this model.
Abstract: Generalized exponential distribution has received some attention in the last few years. Recently, Kundu and Gupta (Advances in Statistical Analysis, 95, 169–185, 2011) and Shoaee and Khorram (Journal of Statistical Planning and Inference, 142, 2203–2220, 2012) introduced an absolute continuous bivariate generalized exponential distribution. In this paper, we propose an absolute coinuous multivariate generalized exponential distribution. The proposed distribution is very flexible, and the joint probability density functions can take different shapes. We provide several properties of this model. Further, it is observed that the multivariate generalized exponential model can be obtained using multivariate Clayton copula. The maximum likelihood estimators are quite difficult to compute in practice. Due to this reason, we propose two step estimation procedure using the copula approach, which are quite easy to implement. Simulation experiments are performed to compare the performances of the two different estimators, and the performances are quite similar in nature particularly for large sample sizes. One multivariate bone mineral density data set has been analyzed for illustrative purposes, and it is observed that the proposed model provides a very good fit to the data set.
10 citations
01 Jan 1975
TL;DR: Several characterizations of the exponential distribution in terms of the variances and the covariances of order statistics in a random sample of size n (n ≥ 2) are made as mentioned in this paper.
Abstract: Several characterizations of the exponential distribution in terms of the variances and the covariances of order statistics in a random sample of size n (n ≥ 2) are made. Analogous characterizations hold for the positive exponential distribution.
10 citations