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 appear] for stochastic orderings of gOS's are contained in our new results.