Estimating the power generalized Weibull Distribution’s parameters using three methods under Type-II Censoring-Scheme

Abstract

A crucial issue is choosing an appropriate model. Additionally, in earlier studies, it was difficult to estimate the unknown variables on the progressing type-II-censoring method. Thus, in this study, a Power Generalised Weibull Distribution (PGWD) has been introduced. This distribution is also known as a generalisation of the Weibull distribution. The Power Generalized Weibull (PGW) parameters have been estimated in this paper utilising the maximum likelihood (ML) approach, the maximum product spacing (MPS) technique, and the Bayesian assessment approach under squared error of loss functions (SELF). The assessment is carried out using progressively type-II censored data, and Monte Carlo Simulation has been utilized to compare the three techniques. The PWGD's Bayes estimators have been computed using the Lindley Approximation (LiA) approach. LiA has been used to present the Bayesian assessment predicated on SELF under the presumption of a natural conjugate-prior. Three alternative optimality metrics, including mean squares of error (MSE), relative efficiency (RE), and bias have been used to identify the best censoring strategy. It was found that Bayesian estimation behaves very better for PGWD, wherein MSE and Bias drop than other approaches, with regard to the natural conjugated prior.

Keywords

• Bayesian estimation
• Power Generalized-Weibull
• Maximum likelihood
• type-II censor data
• Maximum product spacing