A NEW GENERALIZED-UPPER RECORD VALUES-G FAMILY OF LIFETIME DISTRIBUTIONS

Abstract

A new family of lifetime distributions is introduced via distribution of the upper record values, the well-known concept in survival analysisand reliability engineering. Some important properties of the proposed modelincluding quantile function, hazard function, order statistics are obtained in ageneral setting. A special case of this new family is proposed by considering theexponential and Weibull distribution as the parent distributions. In additionestimating unknown parameters of specialized distribution is examined fromthe perspective of the traditional statistics. A simulation study is presentedto investigate the bias and mean square error of the maximum likelihood estimators. Moreover, one example of real data set is studied; point and intervalestimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority ofthe proposed model in terms of the parent exponential distribution over otherknown distributions is shown via the example of real observations.