A note on the characterization of pareto distribution by the hazard rate of upper record values

Abstract

Let {X-i, i = 1 2, ... } be a sequence of independent and identically distributed (iid) random variables with absolutely continuous (with respect to Lebesgue measure) cumulative distribution function (cdf) F(x) with F(1) = 0 and the corresponding probability density function (pdf) f(x). We provide two characterizations of Pareto distribution based on ratios of upper records and properties of hazard rate.