Classical and Bayesian estimation of Kumaraswamy distribution based on type II hybrid censored data

Abstract

‎In the literature‎, ‎different estimation procedures are used for inference about {\color{red} Kumaraswamy} distribution based on complete data sets‎. ‎But‎, ‎in many life-testing and reliability studies‎, ‎a censored sample of data may be available in which failure times of some units are not reported‎. ‎Unlike the common practice in the literature‎, ‎this paper considers non-Bayesian and Bayesian estimation of‎ ‎Kumaraswamy parameters when the data are type II hybrid‎ ‎censored‎. ‎The maximum likelihood estimates (MLE) and its asymptotic variance-covariance matrix are obtained‎. ‎The asymptotic variances and covariances of the MLEs are used to construct approximate confidence‎ ‎intervals‎. ‎In addition‎, ‎by using the parametric bootstrap method‎, ‎the construction‎ ‎of confidence intervals for the unknown parameter is discussed‎. ‎Further‎, ‎the Bayesian estimation of the parameters under‎ ‎squared error loss function is discussed‎. ‎Based on type II hybrid‎ ‎censored data‎, ‎the Bayes‎ ‎estimate of the parameters cannot be obtained explicitly; therefore‎, ‎an approximation method‎, ‎namely Tierney and Kadane's approximation‎, ‎is used to compute the‎ ‎Bayes estimates of the parameters‎. ‎Monte Carlo‎ ‎simulations are performed to compare the performances of the different methods‎, ‎and one real data set is analyzed for illustrative purposes‎.