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Properties of some stochastic orders: A unified study. (English) Zbl 1062.60013

The authors introduce two families of stochastic orders that include the likelihood ratio order, the hazard rate order, and the mean residual life order as special cases. They derive some basic properties and basic closure results for these generalized stochastic orders, as well as some interrelationships among them. The shifted versions of these orders are also studied. Some results in the literature are obtained as special cases of the results in this paper.

MSC:

60E15 Inequalities; stochastic orderings
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