Bayesian estimation of parameters under two parameters extended Marshal-Olkin family of distributions based on different loss functions

Abstract

Estimation of different parameters from two parameters extended Marshall-Olkin distribution was performed based on Lindly approximation and MCMC method under various loss functions. For producing samples from complete conditional distribution parameters, the Metropolis-Hastings algorithm was used. And we have used various some informative and non-informative prior. Based on the  observations of the present study , it was observed that  the Lindley approximation method has provided more approximate estimates from the view of MSE reduction by the MCMC method, and as a result, compatible estimationshave been produced. The optimality of the proposed model is described by using a practical example.