Exact moments of order statistics from a power-function distribution

Abstract

Summary In this note a problem on exact moments of order statistics from a power-function distribution is considered. The characteristic function of the kth order statistic is obtained and moments about the origin of the kth order statistic are expressed in terms of gamma functions. An exact expression for the covariance of any two order statistics Yi < Yj is obtained in terms of beta and gamma functions. Various recurrence relations between the expected values of order statistics are also obtained.