Preservation of Some Aging Properties and Stochastic Orders by Weighted Distributions

By assuming that a random variable X possesses an aging property, we provide conditions under which the corresponding weighted version X 1, with weight function w 1(·), would also possess this aging property. Similarly, by assuming that two random variables X and Y are ordered with respect to a stochastic order, we provide conditions under which the corresponding weighted versions X 1 and Y 2, with weight functions w 1(·) and w 2(·), respectively, preserve this stochastic ordering. We also point out fallacies in the similar results claimed by Jain et al. (1989) and Bartoszewicz and Skolimowska (2006) and correct them.