A general recurrence relation for moments of order statistics in a class of probability distributions and characterizations

Summary In a class of distribution functions, including exponential, power function, Pareto, Lomax, and logistic distributions, a general recurrence relation for moments of order statistics is given. The validity of this identity for certain constants and some sequence of order statistics leads to characterizations of probability distributions. Several recurrence relations and characterization results known from the literature are particular cases of the theorems stated.