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Demonstration of the Use of Lower Partial Moments to Improve Safety‐First Probability Limits
Author(s) -
Atwood Joseph
Publication year - 1985
Publication title -
american journal of agricultural economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.949
H-Index - 111
eISSN - 1467-8276
pISSN - 0002-9092
DOI - 10.2307/1241818
Subject(s) - mathematics , constraint (computer aided design) , upper and lower bounds , moment (physics) , point (geometry) , statistics , mathematical optimization , mathematical analysis , physics , geometry , classical mechanics
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.