On Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings

The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS''s as well as two sub-vectors of $p$-spacings based on two continuous distribution functions. In particular, we apply the new results to obtain some computable bounds on the mean residual life of some unobserved progressive type II censored order statistics.