Some Results on Stochastic Orderings of Generalized Order Statistics and Spacings

Abstract

Generalized order statistics unify the study of order statistics, record values, k-records, Pfeifer’s records and several other cases of ordered random variables. In this paper, we first provide several comparison results for generalized order statistics in terms of the dynamic cumulative residual quantile entropy order. We also prove that when the minimum of random vectors of generalized order statistics is increasing mean residual life (IMRL), the spacings of generalized order statistics are ordered by variance, and the covariance between successive spacings is nonnegative. The normalized spacings of generalized order statistics from two sample sequences are also compared with respect to the mean residual life and the excess wealth orders.

Keywords

• Generalized order statistics; Mean residual life order; Excess wealth order; Dynamic cumulative residual quantile entropy order; DFR; IFR; DMRL; IMRL.