Optimal sampling and statistical inferences for Kumaraswamy distribution under progressive Type-II censoring schemes

In this paper, we study non-Bayesian and Bayesian estimation of parameters for the Kumaraswamy distribution based on progressive Type-II censoring. First, the maximum likelihood estimates and maximum product spacings are derived. In addition, we derive the asymptotic distribution of the parameters and the asymptotic confidence intervals. Second, Bayesian estimators under symmetric and asymmetric loss functions (Squared error, linear exponential, and general entropy loss functions) are also obtained. The Lindley approximation and the Markov chain Monte Carlo method are used to derive the Bayesian estimates. Furthermore, we derive the highest posterior density credible intervals of the parameters. We further present an optimal progressive censoring scheme among different competing censoring scheme using three optimality criteria. Simulation studies are conducted to evaluate the performance of the point and interval estimators. Finally, one application of real data sets is provided to illustrate the proposed procedures.

Automated summary

In this paper, the non-Bayesian and Bayesian estimation of parameters for the Kumaraswamy distribution based on progressive Type-II censoring is studied. The maximum likelihood estimates, maximum product spacings, and asymptotic distribution of the parameters are derived. Bayesian estimators under symmetric and asymmetric loss functions are obtained using the Lindley approximation and Markov chain Monte Carlo method. The performance of the point and interval estimators is evaluated through simulation studies.