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Dominance Relations Among Standardized Variables

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Author Info

  • Frank Milne

    (Department of Economics, Queen's University, Kingston, Ontario, Canada K7M 3N6)

  • Edwin H. Neave

    (School of Business, Queen's University, Kingston, Ontario, Canada K7M 3N6)

Abstract

This paper examines stochastic dominance relations among discrete random variables defined on a common integer domain. While these restrictions are minimal, they lead both to new theoretical results and to simpler proofs of existing one. The new results, obtained for dominance criteria of any degree, generalize an SSD result of Rothschild-Stiglitz to describe how for any dominance criterion a dominated variable is equal in distribution to a dominated variable plus perturbation terms. If the variables are comparable under FSD the perturbations are downward shift terms, while under SSD (TSD) all but two (three) of the perturbations are zero mean disturbance terms (noise). Under SSD the remaining perturbations are shift terms and under TSD noise and shift terms. However, under either SSD or TSD these remaining terms are identically zero if the variables to be compared have equal means. The paper also finds new proofs of well known results relating dominance criteria to preferences.

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File URL: http://dx.doi.org/10.1287/mnsc.40.10.1343
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 40 (1994)
Issue (Month): 10 (October)
Pages: 1343-1352

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Handle: RePEc:inm:ormnsc:v:40:y:1994:i:10:p:1343-1352

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Related research

Keywords: stochastic dominance; decision theory; comparing random variables;

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Cited by:
  1. Dong, Lingxiu & Kouvelis, Panos & Su, Ping, 2013. "Global facility network design in the presence of competition," European Journal of Operational Research, Elsevier, vol. 228(2), pages 437-446.
  2. Miller-Hooks, Elise & Mahmassani, Hani, 2003. "Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 146(1), pages 67-82, April.
  3. Dong, Lingxiu & Kouvelis, Panos & Su, Ping, 2014. "Operational hedging strategies and competitive exposure to exchange rates," International Journal of Production Economics, Elsevier, vol. 153(C), pages 215-229.
  4. Li, Xiaoming, 2008. "Demand evolution in stochastic inventory systems: Riskiness increase," International Journal of Production Economics, Elsevier, vol. 116(2), pages 182-189, December.
  5. Seifert, Ralf W. & Thonemann, Ulrich W. & Sieke, Marcel A., 2006. "Integrating direct and indirect sales channels under decentralized decision-making," International Journal of Production Economics, Elsevier, vol. 103(1), pages 209-229, September.
  6. Chakravarty, Satya R. & Zoli, Claudio, 2012. "Stochastic dominance relations for integer variables," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1331-1341.

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