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Stochastic dominance with imprecise information

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  • Montes, Ignacio
  • Miranda, Enrique
  • Montes, Susana

Abstract

Stochastic dominance, which is based on the comparison of distribution functions, is one of the most popular preference measures. However, its use is limited to the case where the goal is to compare pairs of distribution functions, whereas in many cases it is interesting to compare sets of distribution functions: this may be the case for instance when the available information does not allow to fully elicitate the probability distributions of the random variables. To deal with these situations, a number of generalisations of the notion of stochastic dominance are proposed; their connection with an equivalent p-box representation of the sets of distribution functions is studied; a number of particular cases, such as sets of distributions associated to possibility measures, are investigated; and an application to the comparison of the Lorenz curves of countries within the same region is presented.

Suggested Citation

  • Montes, Ignacio & Miranda, Enrique & Montes, Susana, 2014. "Stochastic dominance with imprecise information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 868-886.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:868-886
    DOI: 10.1016/j.csda.2012.07.030
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    Cited by:

    1. Jiang, Yanping & Liang, Xia & Liang, Haiming & Yang, Ningman, 2018. "Multiple criteria decision making with interval stochastic variables: A method based on interval stochastic dominance," European Journal of Operational Research, Elsevier, vol. 271(2), pages 632-643.
    2. Černý, Michal & Hladík, Milan, 2014. "The complexity of computation and approximation of the t-ratio over one-dimensional interval data," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 26-43.
    3. Montes, Ignacio & Salamanca, Juan Jesús & Montes, Susana, 2020. "A modified version of stochastic dominance involving dependence," Statistics & Probability Letters, Elsevier, vol. 165(C).
    4. Yunna Wu & Chuanbo Xu & Hu Xu, 2016. "Optimal Site Selection of Tidal Power Plants Using a Novel Method: A Case in China," Energies, MDPI, vol. 9(10), pages 1-26, October.

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