摘要：One notion of stochastic comparisons of non-negative random variables based on ra- tios of n th derivative of Laplace transforms (n-Laplace transform order or shortly ≤ n -Lt-r order) is introduced by Mulero et al. (2010). In addition, they studied some of its applications in frailty models. In this paper, we have fo cused on some further properties of this order. In particular, we have shown that ≤ n -Lt-r order implies dual weak likelihood ratio order (≤ DWLR order). Moreover, ≤ n -Lt-r order, under certain circumstances, implies likeliho od ratio order (≤ lr order). Finally, the L (n) ( ˉ L (n) )-class of life distribution is proposed and studied. This class reduces to L ( ˉ L)-class if we take n = 0.
关键词：likelihood ratio order; hazard rate order; shock models; dual weak likelihood ratio ; ordering; totally positive of order 2 ( TP ; 2 ; ).
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