The power-linear hazard rate distribution andestimation of its parameters under progressivelytype-II censoring

Abstract

In this paper, we introduce a class of distributions which generalizesthe power hazard rate distribution and is obtained by combining thelinear and power hazard rate functions. This class of distributions,which is called the power-linear hazard rate distribution, is simpleand flexible and contains some important lifetime distributions. Themaximum likelihood estimators of the parameters using the Newton-Raphson (NR) and the expectation-maximization (EM) algorithms andthe Bayes estimators of the parameters under squared error loss (SEL),linear-exponential (LINEX) and Stein loss functions are obtained basedon progressively type-II censored sample. Also, we obtain the asymp-totic confidence interval and some bootstrap confidence intervals andconstruct the HPD credible interval for the parameters. A real data setis analyzed and observed that the present hazard rate distribution canprovide a better fit than other three-parameter distributions. Finally, aMonte Carlo simulation study is conducted to investigate and comparethe performance of different types of estimators presented in this paper.