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

摘要

?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?.