Characterization of Some Distributions by Inequalities on Failure Rate

Characterizing distributions is the process of nding the unique properties that distinguish a particular distribution from others. there are various methods for doing this, such as using moments, maximum entropy, hazard rate, and so on. nanda (2010) used failure rate and mean residual life functions to characterizing some distributions. in this paper, we extend the results of nanda (2010). we characterize the pareto, exponential, and rayleigh distributions by rening the main results of thatpaper. we take some inequalities from that paper and propose a new inequality. then, we raise both sides of the inequalities to some power and show that equality holds if and only if certain distributions are characterized.