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A note on relationships between some univariate stochastic orders and the corresponding joint stochastic orders

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  • Franco Pellerey
  • Saeed Zalzadeh

Abstract

In order to take into account any possible dependence between alternatives in optimization problems, bivariate characterizations of some well-know univariate stochastic orders have been defined and studied by Shanthikumar and Yao (Adv Appl Probab 23:642–659, 1991 ). These characterizations gave rise to new stochastic comparisons, commonly called joint stochastic orders, which are equivalent to the original ones under assumption of independence, but are different whenever the variables to be compared are dependent. In this note we provide sufficient conditions on the survival copula describing the dependence among the compared variables such that the standard stochastic orders imply the corresponding joint stochastic orders, and viceversa. Also, simple conditions for joint stochastic orders between the components of random vectors defined through multivariate frailty models are provided. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Franco Pellerey & Saeed Zalzadeh, 2015. "A note on relationships between some univariate stochastic orders and the corresponding joint stochastic orders," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 399-414, May.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:4:p:399-414
    DOI: 10.1007/s00184-014-0509-5
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    References listed on IDEAS

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    1. Hua, Lei & Cheung, Ka Chun, 2008. "Stochastic orders of scalar products with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 865-872, June.
    2. Félix Belzunce & Eva-María Ortega & Franco Pellerey & José Ruiz, 2007. "On rankings and top choices in random utility models with dependent utilities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 197-212, September.
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    Cited by:

    1. Li, Chen & Li, Xiaohu, 2017. "Preservation of weak stochastic arrangement increasing under fixed time left-censoring," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 42-49.
    2. Zalzadeh, Saeed & Pellerey, Franco, 2016. "A positive dependence notion based on componentwise unimodality of copulas," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 51-57.
    3. Enrico Bibbona & Laura Sacerdote & Emiliano Torre, 2016. "A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 765-783, September.
    4. Yinping You & Xiaohu Li & Rui Fang, 2021. "On coverage limits and deductibles for SAI loss severities," Annals of Operations Research, Springer, vol. 297(1), pages 341-357, February.

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