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

Franco Pellerey () and Saeed Zalzadeh ()

Metrika: International Journal for Theoretical and Applied Statistics, 2015, vol. 78, issue 4, 399-414

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

Keywords: Usual stochastic order; Likelihood ratio order; Hazard rate order; Joint stochastic orders; Copulas; Frailty models (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00184-014-0509-5

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