Estimation and application for a new extended Weibull distribution

In this paper, a new extended Weibull distribution with one scale parameter and two shape parameters is introduced. It is investigated that the new model has increasing and upside-down bathtub shaped hazard rate functions. The properties of skewness and Weibull type probability plot are discussed that serve as a tool for model identification. Given progressively type-II censored data, the maximum likelihood estimators of the parameters and corresponding confidence intervals are discussed; then the Gibbs sampling technique is derived to construct the Bayesian estimators of the parameters and the credible intervals based on the assumption that the prior of the scale parameter is gamma density function and priors of the shape parameters are the log-concave density function under the square error loss function. Two real data sets are analyzed for illustrating the application of the new model and the proposed Bayesian approach.