Estimating the Parameters of Kumaraswamy Distribution Using Progressively Censored Data

Abstract

Abstract In this paper, the maximum likelihood, Bayes, and parametric bootstrap methods are used for estimating the unknown parameters, as well as some lifetime parameters reliability and hazard functions, based on progressively Type II right-censored samples from a two-parameter Kumaraswamy distribution. Approximate confidence intervals (ACIs) for the unknown parameters, as well as reliability and hazard functions, are constructed based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators (MLEs) and log-transformed MLEs. In addition, two bootstrap CIs are also proposed. The classical Bayes estimates cannot be obtained in explicit form, so we propose to apply the Markov chain Monte Carlo (MCMC) technique to tackle this problem, which allows us to construct the credible interval of the involved parameters. Gibbs within the Metropolis–Hasting sampling procedure has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters, as well as reliability and hazard functions, have been computed. The results of the Bayes method are obtained under both the balanced squared error (BSE) loss and balanced linear-exponential (BLINEX) loss. A real-life data set is analyzed to illustrate the proposed methods of estimation. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with MLEs and two bootstrap estimates, also to compare the performance of different corresponding CIs considered.