Resumen de An Upper Bound for the Expected Difference between Order Statistics

Manuel Lopez, James Marengo

• It is well known that the order statistics of a random sample from the uniform distribution on the interval [0, 1] have Beta distributions. In this paper we consider the order statistics of a random sample of n data points chosen from an arbitrary probability distribution on the interval [0, 1]. For integers k and l with 1 ?k ? l ? n we find an attainable upper bound for the expected difference between the order statistics Yl and Yk . This upper bound depends on the choice of k and l but does not depend on the distribution from which the data are obtained. We suggest a possible application of this result and we discuss some of its special cases.