Relations for order statistics from non-identical logistic random variables and assessment of the effect of multiple outliers on the bias of linear estimators

Abstract

In this paper, we establish some relations for the single moments of order statistics arising from n independent and non-identically distributed logistic random variables. These relations are then used to deduce a set of recurrence relations for the moments of order statistics from the multiple-outlier logistic model (with a slippage of p observations). The moments of order statistics from the p-outlier model are expressed in terms of the corresponding quantities from ( p - 1 ) -outlier and ( p - 2 ) -outlier models. We then use these recurrence relations along with the corresponding i.i.d. results originally derived by Shah [1970. Note on moments of a logistic order statistics, Ann. Math. Statist. 41, 2151–2152.] and the results for the single outlier model discussed by Balakrishnan [1992a. Relationships between single moments of order statistics from non-identically distributed variables. In: Sen, P.K., Salama, I.A. (Eds.), Order Statistics and Nonparametrics: Theory and Applications. Elsevier, Amsterdam, pp. 65–78.] to compute the bias of various linear estimators of the location and scale parameters of the logistic distribution in the presence of multiple outliers.