Bayesian Parameter Estimation for Geometric Process with Rayleigh Distribution

The main purpose of this study is to deal with the parameter estimation problem for the geometric process (GP) when the distribution of the first occurrence time of an event is assumed to be Rayleigh. For this purpose, maximum likelihood and Bayesian parameter estimation methods are discussed. Lindley and MCMC approximation methods are used in Bayesian calculations. Additionally, a novel method called the Modified-Lindley approximation has been proposed as an alternative to the Lindley approximation. An extensive simulation study was conducted to compare the performances of the prediction methods. Finally, a real data set is analyzed for illustrative purposes.