Bayesian estimation of $$R=P[Y<X]$$ for inverse Lomax distribution under progressive type-II censoring scheme

Abstract

In this article, we propose the estimation procedure to estimate the stress-strength reliability parameter $$R=P[Y<X]$$ for inverse Lomax distribution when available information on strength (X) and stress (Y) are progressively type-II censored. Maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator are derived in the presence of progressive type-II censoring scheme. It is obvious that censoring adds complexity; thus the estimators do not appear in the explicit form. Therefore, numerical approximation techniques have been used to secure the estimates of the parameters. The comparison among the proposed estimators are made by performing the Monte Carlo simulation study, and finally three data sets have been used to demonstrate the study in real life.