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Along this paper, we study the relationship between the unimodality of the likelihood ratio and the behaviour of the ratio of two survival functions. The results provide sufficient conditions for both the hazard rated order when the likelihood ratio order does not hold and the mean residual life order when the hazard rate order does not hold. Examples where these results can be applied are also given.
This paper is devoted to the study of the comparison of generalized order statistics in terms of the total time on test transform and the excess wealth orders. We provide some extensions of previous results in the literature for usual order statistics and generalized order statistics. These results involve results for the minimum of a random vector of generalized order statistics.
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