Some properties of the residual lifetime of progressively Type-II right censored order statistics

In the present paper we propose a new concept of the residual lifetime of progressively Type-II right censored order statistics (PCOS) and study some of its properties. Some new stochastic comparisons are made on the residual lifetimes of PCOS. The case when the behavior of the data generator F, in terms of different aging concepts, is given the behavior of the residual lifetimes of PCOS is investigated. We also concentrate on the mean of the residual lifetime of the PCOS. Some characterizations of the generalized Pareto distribution based on the mean of the residual lifetime of PCOS are also presented.