Advances and Applications in Statistics
Volume 54, Issue 2, Pages 327 - 344
(February 2019) http://dx.doi.org/10.17654/AS054020327 |
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NON BAYESIAN AND BAYESIAN ESTIMATION FOR THE BIVARIATE GENERALIZED LINDLEY DISTRIBUTION
Rania M. Shalabi
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Abstract: In this paper, we extend Marshall and Olkin’s bivariate exponential model to the bivariate generalized Lindley (BGL) distribution. The generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The cumulative distribution function, the probability density function and the conditional distribution of the BGL distribution are reached. The maximum likelihood estimation procedure is derived for the estimation of the BGL parameters, when all parameters are unknown and also obtain the observed Fisher information matrix. On the other hand, there is a special case of the distribution of the BGL distribution is obtained in a closed form when one of the parameters is known. Finally, we consider the Bayesian analysis of the Marshall-Olkin bivariate generalized Lindley distribution. The Bayes estimators are reached with respect to the squared error loss function and the prior distributions allow for prior dependence among the components of the parameter vector. When the shape parameter is known, the Bayes estimators of the unknown parameters can be reached in explicit forms under the assumptions of independent priors. By the end, a simulation study was analyzed. |
Keywords and phrases: generalized Lindley distribution, Bayesian inference, maximum likelihood estimators, Fisher information matrix.
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