The power-linear hazard rate distribution and estimation of its parameters under progressively type-II censoring

In this paper, we introduce a class of distributions which generalizes the power hazard rate distribution and is obtained by combining the linear and power hazard rate functions. This class of distributions, which is called the power-linear hazard rate distribution, is simple and flexible and contains some important lifetime distributions. The maximum likelihood estimators of the parameters using the Newton-Raphson (NR) and the expectation-maximization (EM) algorithms and the Bayes estimators of the parameters under squared error loss (SEL), linear-exponential (LINEX) and Stein loss functions are obtained based on progressively type-II censored sample. Also, we obtain the asymptotic confidence interval and some bootstrap confidence intervals and construct the HPD credible interval for the parameters. A real data set is analyzed and observed that the present hazard rate distribution can provide a better fit than other three-parameter distributions. Finally, a Monte Carlo simulation study is conducted to investigate and compare the performance of different types of estimators presented in this paper.