A new family of lifetime distributions in terms of cumulative hazard rate function

Abstract

In the present paper, a new family of lifetime distributions is introduced according to cumulative hazard rate function, the well-known concept in survival analysis and reliability engineering. Some important properties of proposed model including survival function, quantile function, hazard function, order statistic and some results of stochastic ordering are obtained in general setting. An especial case of this new family is introduced by considering Weibull distribution as the parent distribution; in addition estimating unknown parameters of specialized model will be examined from the perspective of Bayesian and classic statistics. Moreover, three examples of real data sets: complete, right-censored and progressively type-I interval-censored data are studied; point and interval estimations of all parameters are obtained. Finally, the superiority of proposed model in terms of parent Weibull distribution over other fundamental statistical distributions is shown via complete real observations.