Recurrence Relations for Quotient Moment of Generalized Pareto Distribution Based on Generalized Order Statistics and Characterization

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.