BAYESIAN ESTIMATION OF THE PARAMETER OF GENERALIZED EXPONENTIAL DISTRIBUTION USING MARKOV CHAIN MONTE CARLO METHOD IN OPEN BUGS FOR INFORMATIVE SET OF PRIORS
Keywords:
Generalized Exponential (GE) Distribution, parameter estimation, informative set of priors, Maximum likelihood Estimation (MLE), Bayesian Estimation in Open Bugs, Markov Chain Monte Carlo (MCMC) MethodAbstract
The two-parameter generalized exponential (GE) distribution was introduced and studied quite extensively by (Gupta and Kundu (1999), (2001a) and (2001b)). and Ahsanullah (2001) and Raqab (2002) studied the properties of order and record statistics from the GE distribution and their inferences, respectively. Gupta and Kundu (2003) used the ratio of the maximized likelihoods (RML) in discriminating between the Weibull and GE distributions. The two parameters of a GE distribution represent the scale and the shape parameters and because of the scale and shape parameters.
The Markov Chain Monte Carlo (MCMC) method is used to estimate the parameters of a generalized exponential distribution based on a complete sample. The MCMC methods have been shown to be easy to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. The R functions are developed to study the statistical properties of the distribution and the output analysis of MCMC samples generated from Open BUGS. The maximum-likelihood estimation (MLE) is the most used method for parameter estimation. We also compute the maximum likelihood estimate and associated confidence intervals to compare the performance of the Bayes estimators with the classical estimator’s construction of associated probability intervals. We also develop a module dgen (alpha,lamda) which is written in component Pascal, enable to perform full Bayesian analysis of generalized exponential distribution. The proposed methodology can be applied for empirical modeling, which includes estimation of parameters, model validation and comparison. A real data set is considered for illustration purpose under gamma priors.
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