Stochastic Properties of the Weighted Hazard Rate Order

Abstract

The hazard rate order between two weighted distributions with a given weight function is considered as a new stochastic order called weighted hazard rate order. The influences of biased sampling methods on properties of the hazard rate order are usefully pointed out with this weighted order. We first obtain some basic properties of the weighted hazard rate order and then develop some useful preservation properties of it with respect to monotone transformations, mixture of distributions, convolution of distributions, order statistics and residual lifetime of distributions. A few examples are also presented to show the usefulness of the results achieved in the paper.