Weaker shape conditions on likelihood ratios, including unimodality, limited sign changes with negative tail, or superlevel-set criteria, suffice for endpoint criteria in hazard-rate and usual stochastic orders.
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Stochastic Ordering under Weaker Likelihood-Ratio Shape Conditions
Weaker shape conditions on likelihood ratios, including unimodality, limited sign changes with negative tail, or superlevel-set criteria, suffice for endpoint criteria in hazard-rate and usual stochastic orders.