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In reliability and life testing studies, the topic of estimating hazard ratehas received great attention in recent years since an estimate of hazard rateis a quite useful tool for making decisions. Some works have includednonparametric approaches while some have considered parametric structuralmodels for complete as well as censored data sets; see Meeker et al. (1992),Antoniadis and Gr\'egoire (1999), Rai and Singh (2003), Bezandry et al. (2005),Brunel and Comte (2008), and Mahapatra et al. (2012). Depending on the shapesof the hazard rate, efficiencies differ markedly across proposed estimators.This situation is remarkable especially when different estimation techniquesare utilized for unknown parameters of underlying distributions in parametricapproaches. That is, estimated hazard rate (and also reliability) at a specifictime point t as functions of these estimators leads to inconsistent coverageprobabilities as distributional convergence of hazard rate estimator may not beat the desired rate for certain sample sizes.  This manuscript focuses on the estimation of monotone hazard rate when thedistribution of concern is of location-scale type. A very simple and efficientapproximation of hazard rate for a complete sample is introduced as a functionof order statistics, which allows a fast convergence to the asymptoticdistribution while achieving highly accurate coverage probabilities forconfidence intervals (CI). Efficiency of the method is demonstrated onsimulation studies by considering a number of location-scale distributionshaving various hazard shapes. We also consider the case of censored samples byincorporating the predicted future order statistics into the picture.

Hazard rate estimation for location-scale distributions under complete and censored data