Kernel monotonicity and concavity plus tail-conditional mean inequalities characterize multiple stochastic orders in parametric density families, extending to compound sums and nonmonotone cases.
Comparison Methods for Stochastic Models and Risks , publisher =
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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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Kernel Characterisations of Stochastic Orders Within Parametric Density Families
Kernel monotonicity and concavity plus tail-conditional mean inequalities characterize multiple stochastic orders in parametric density families, extending to compound sums and nonmonotone cases.
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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.