Bayesian Inference on the Generalized Shape-Scale Family based on Kernel Prior

Abstract

Abstract In statistical inference, Bayesian inference is widely used in estimating the distribution parameters despite of it is subjective to prior information other than data that produces undesirable conclusions. Thus, the main objective of this paper to apply the Bayes theorem to the conditional distribution of pivotal functions using kernel priors for those pivotal functions. The conditional inference has been used for estimating the generalized shape-scale family parameters, based on a generalized progressive hybrid-censoring scheme, and compared to Bayesian estimates, via Monte Carlo simulations. The simulation results indicated that conditional inference is highly efficient and provides better estimates than Bayesian inference using different loss functions. Finally, two real data sets have been given to demonstrate the efficiency of the proposed methods.