Estimation procedures for Kumaraswamy distribution parameters under adaptive type-II hybrid progressive censoring

This paper describes the point and interval estimation of the unknown parameters of Kumaraswamy (Ku) distribution under the adaptive Type-II hybrid progressive censored samples. First, we obtain the maximum likelihood estimation (MLE) of the parameters using Newton-Raphson (NR) method, expectation maximization (EM) and stochastic EM (SEM) algorithms. In addition, we derive the asymptotic distribution of the parameters and the asymptotic confidence intervals. Moreover, two bootstrap confidence intervals are achieved. Second, the Bayesian estimation of the parameters is approximated by using the Markov Chain Monte Carlo (MCMC) algorithm and Lindley's method due to the lack of explicit forms. Furthermore, the highest posterior density (HPD) credible intervals of the parameters are derived. Finally, the different proposed estimations have been compared by the simulation studies and a practical data set is analyzed to illustrative aims.