Bayesian Inference for Geometric Process With Generalized Exponential Distribution

Abstract

There is no doubt that precise and effective estimation of model parameters is crucial in many fields. In this study, the Bayesian and classical estimators for the geometric process are discussed under the assumption that X1 has a generalized exponential distribution with parameters alpha,lambda. The maximum likelihood estimation method is used in classical parameter estimation. Then, the asymptotic distributions are constructed based on the maximum likelihood estimator. A test statistic is also developed based on maximum likelihood estimators for testing whether a=1 or not. The loss function and prior distribution play an important role in Bayesian inference. Therefore, Bayes estimators of the unknown model parameters are obtained under symmetric (squared error loss function) and asymmetric (linear exponential, and general entropy) loss functions using uniform and gamma priors on the ratio a and alpha,lambda parameters, respectively. Lindley and MCMC approximation methods are used for Bayesian calculations. An extensive Monte Carlo simulation study compared the efficiencies of classical estimators with Bayes estimators. It is seen that the Bayes estimators perform better than the classical estimators. A real-life example is also presented for application purposes.