Bounds for means and variances of progressive type II censored order statistics

By applying different methods, bounds for expected values and variances of progressive type II censored order statistics are derived. Since ordinary order statistics are contained in the model, well-known bounds for their moments are obtained as particular cases. The method of the greatest convex minorant leads to close bounds for means of progressive type II censored order statistics, which are even new in the particular set-up of ordinary order statistics. Numerical examples are shown in order to compare bounds and exact values for means w.r.t. underlying rectangular and normal distributions.