Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data

Abstract

This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods.

Comparison of Estimation Methods for Reliability Function for Family of Inverse Exponentiated Distributions under New Loss Function

“…Dutta et al [10] obtained useful estimation results for a general family of inverted exponentiated distributions under unified hybrid censoring, with partially observed competing risk data. Hashem et al [11] estimated the reliability of the IER distribution by using the Bayesian method under generalized progressive hybrid censored data, among others. Due to its definition, it is noted that some conventional lifetime models belong to this general family.…”