Bayesian Inference for Geometric Process with Generalized Exponential Distribution
Asuman Yılmaz · Fluctuation and Noise Letters · 2025
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 [Formula: see text] has a generalized exponential distribution with parameters [Formula: see text]. 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 [Formula: see text] 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 [Formula: see text] 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.