Estimation the Reliability Function and Hazard Rate Function of Pham Distribution under Balanced Joint Progressive Type-II Censored Data

Abstract

This paper investigates the estimation of the reliability and hazard functions of the Pham distribution under a balanced joint progressive type-II censoring scheme. Two estimation approaches are considered: maximum likelihood estimation (MLE) and maximum product of spacings estimation (MPSE). In addition to point estimation, interval estimation is carried out by constructing approximate confidence intervals using MLE and MPSE methods. {Moreover, bootstrap-based confidence intervals are obtained using three techniques: the percentile bootstrap, the Student’s-t bootstrap and the normal distribution bootstrap.} The problem of selecting an optimal censoring scheme is also addressed. A comprehensive Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the proposed estimators in terms of both point and interval estimation. Finally, the practical applicability of the proposed methods is illustrated through the analysis of a real-life data set.