Estimation of the Kumaraswamy distribution parameters using the E-Bayesian method

The Kumaraswamy distribution (KD) is widely applied for modeling data in practical domains, such as medicine, engineering, economics, and physics. The present work proposes the Bayesian estimators of KD parameters through the use of type-II censoring data. Both E-Bayesian and Bayesian estimation approaches are briefly described, along with several loss functions, namely, linex loss function (LLF), weighted linex loss function (WLLF), and composite linex loss function (CLLF). In the Bayesian framework, gamma distribution has been utilized as a conjugate distribution in view of finding theoretical results. The E-Bayesian estimators for the hyperparameter using different distributions are developed. Moreover, a novel loss function referred to as the weighted composite loss function (WCLLF) in the estimation perspective is established. Finally, the Monte Carlo simulation approach is carried out to reveal that the new suggested loss function outperforms several counterparts in determining the shape parameter of the KD.