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Dominance Relations Among Standardized Variable

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  • Frank Milne
  • Edwin H. Neave

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 ones. 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 preference.

Suggested Citation

  • Frank Milne & Edwin H. Neave, 1993. "Dominance Relations Among Standardized Variable," Working Paper 877, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:877
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    Cited by:

    1. Li, Xiaoming, 2008. "Demand evolution in stochastic inventory systems: Riskiness increase," International Journal of Production Economics, Elsevier, vol. 116(2), pages 182-189, December.
    2. Satya R. Chakravarty & Claudio Zoli, 2019. "Stochastic Dominance Relations for Integer Variables," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 211-222, Springer.
    3. 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.
    4. 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.
    5. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    6. Gökbayrak, Esra & Kayış, Enis, 2023. "Single item periodic review inventory control with sales dependent stochastic return flows," International Journal of Production Economics, Elsevier, vol. 255(C).
    7. Lingxiu Dong & Panos Kouvelis & Ping Su, 2010. "Global Facility Network Design with Transshipment and Responsive Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 278-298, February.
    8. 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.
    9. 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.
    10. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.

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