Some New Results on Stochastic Orderings between Generalized Order Statistics

In this paper we specify the conditions on the parameters of pairs of gOS s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. [Probab. Engrg. Inform. Sci. 2002, 16, 471-484] and Belzunce et al, [Probab. Engrg. Inform. Sci. (2004), to appea~ for stochastic orderings of gOS s are contained in our new results.