Performance of Estimates of Reliability Parameters for Compound Rayleigh Progressive Type II Censored Data

Abstract

This paper develops Bayesian analysis in the context of progressively Type II censored data from the two-parameter compound Rayleigh distribution. The maximum likelihood and Bayes estimates along with the associated posterior risks are derived for unknown reliability parameters under the balanced logarithmic loss and balanced general entropy loss functions. A practical example and simulation study have been considered to illustrate the proposed estimation methods and compare the performance of derived estimates based on maximum likelihood and Bayesian frameworks. The study indicates that Bayesian approach is more preferable over the maximum likelihood approach for estimation of the reliability parameters, while in Bayesian approach, a balance general entropy loss function can effectively be employed.

Keywords: Maximum likelihood estimation, Bayes estimation, balanced logarithmic loss function, balanced general entropy loss function, posterior risk, Monte Carlo simulation.