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Department of Statistics, Yazd University, Yazd, Iran
Abstract:   (495 Views)

‎In this paper‎, ‎we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions‎.

‎This new class contains the bivariate generalized exponential-Poisson‎, ‎bivariate generalized exponential-logarithmic‎, ‎bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as special‎ ‎cases‎. ‎We derive different properties of the proposed class of distributions‎. ‎It is observed that the proposed class of‎ ‎bivariate distributions is a very flexible class of distribution functions‎. ‎The joint probability density functions can have‎ ‎variety of shapes‎. ‎It can be bimodal as well as heavy tail also‎. ‎This distribution has five parameters‎. ‎The maximum likelihood‎ ‎estimators of the parameters cannot be obtained in closed form‎. ‎We propose to use EM algorithm to compute the maximum‎ ‎likelihood estimators of the unknown parameters‎. ‎It is observed that the proposed EM algorithm can be implemented very‎ ‎easily in practice‎. ‎One data set has been analyzed for illustrative purposes‎. ‎It is observed that‎ ‎the proposed model and the EM algorithm work quite well in practice‎.

Type of Study: Original Paper | Subject: 62Exx: Distribution theory
Received: 2017/03/13 | Accepted: 2017/12/7 | Published: 2017/12/7