Higher order moments of order statistics from INID symmetric random variables

In this paper we present analogues of Balakrishnan's (1989) relations that relate the triple and quadruple moments of order statistics from independent and nonidentically distributed (I.NI.D.) random variables from a symmetric distribution to those of the folded distribution. We then apply these results, along with the corresponding recurrence relations for the exponential distribution derived recently by Childs (2003), to study the robustness of the Winsorized variance.