Empirical Bayes Estimates of Rayleigh Distribution with Ewmel and Logarithmic Loss Functions for Censored Samples

Abstract

In this paper, empirical Bayes estimates of reliability performances are derived when the data are progressively Type II censored from a Rayleigh distribution. These estimates are derived under exponentially weighted minimum expected loss (EWMEL) and logarithmic loss functions, and compared with the corresponding maximum likelihood estimates in terms of absolute bias and estimated risk. A real data set is presented to illustrate the proposed estimation method, and a Monte Carlo simulation study is carried out to investigate the accuracy of derived estimates. The study shows that the empirical Bayesian estimation outperforms the maximum likelihood estimation.

Keywords: Empirical Bayes estimation, Progressively Type II censored samples, EWMEL and logarithmic loss functions.

2000 Mathematics Subject Classification. 62C12, 62N01, 62F10, 62F15, 62N05