Statistical inferences for new Weibull-Pareto distribution under an adaptive type-ii progressive censored data

In this paper, we obtain the maximum likelihood, Bayes and parametric bootstrap estimators for the parameters of a new Weibull-Pareto distribution (NWPD) and some lifetime indices such as reliability function S(t), failure rate h(t) function and coefficient of variation CV are obtained. The previous methods are studied in the case of an adaptive Type-II progressive censoring (Ada-T-II-Pro-C). Approximate confidence intervals (ACIs) of the unknown parameters are constructed based on the asymptotic normality of maximum likelihood estimators (MLEs). Bayes estimates and the symmetric credible intervals (CRIs) of the unknown quantities are calculated based on the Gibbs sampler within MetropolisI-lasting (M-H) algorithm procedure. The results of Bayes estimates are obtained under the consideration of the informative prior function with respect to the squared error loss (SEL) function. Two numerical examples are presented to illustrate the proposed methods, one of them is a simulated example and the other is a real life example. Finally, the performance of different Bayes estimates are compared with maximum likelihood (ML) and two parametric bootstrap estimates, through a Monte Carlo simulation study.