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Some Characterizations on Generalized Pareto Distributions

Abstract Generalized Pareto distributions (GPD) play an important role in reliability, extreme value theory, and other branches of statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In the present article, we will obtain some characterizations results on GPD. We first propose a new definition for multiplicative lack of memory (MLM) property in terms of mean residual life function and show that, under some mild conditions, the distribution of a continuous non negative, random variable X satisfies in the proposed property if it is a member of GPD. Then, we give a characterization result on GPD based on proportionality of the hazard rate (HR) of a continuous random variable X and the HR of corresponding weighted distribution (for some weight function). We also prove a characterization result on GPD based on the minimum of a random sample.