Demonstration of the Use of Lower Partial Moments to Improve Safety‐First Probability Limits
提出一种利用低阶偏矩的随机不等式，生成安全优先概率的严格上界，相比切比雪夫和均值-半方差不等式更不保守，并开发了优化模型中的约束条件。
Abstract A general stochastic inequality is presented which utilizes lower partial moments to generate sharp upper bounds on safety‐first type probabilities. Alternative forms of the inequality often generate less conservative probability bounds than Chebychev's mean‐standard error and Berck and Hihn's mean‐semivariance inequalities. Of particular interest is the linear lower partial moment version which utilizes absolute deviations below a fixed reference point. A constraint is developed which, if enforced in an optimization model, guarantees that safety‐first probability concerns are satisfied while selecting the least constraining level for the reference point.