Bayesian and Non-Bayesian Estimation for the Shape Parameters of New Versions of Bivariate Inverse Weibull Distribution based on Progressive Type II Censoring

Abstract

The inverse Weibull (IW) distribution can be applied to a wide range of situations including applications in ecology, medicine, and reliability. Moreover, IW distribution gives a good fit to survival data such as the times to breakdown of an insulating fluid subject to the action of constant tension. In this paper, two new versions of the bivariate inverse Weibull distribution (BIW) are introduced depending on, the change of the shape parameters as members of a bivariate reversed hazard power parameter family of distributions, which are defined based on Marshal-Olkin and FGM copulas. MlE and Bayesian estimation methods are considered to estimate the unknown parameters for both BIW models based on progressive Type II censoring. Moreover, asymptotic, credible, and bootstrap confidence intervals for the unknown parameters are evaluated in both MLE and Bayesian Estimation for each BIW model. A numerical comparison will be considered for the two BIW models based on real and simulated data in the presence of progressive Type II censored samples.