Multidimensional stochastic ordering and associated random variables

Multidimensional stochastic ordering and associated random variables

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Article ID: iaor1989365
Country: United States
Volume: 37
Issue: 3
Start Page Number: 478
End Page Number: 487
Publication Date: May 1989
Journal: Operations Research
Authors:
Keywords: probability
Abstract:

This paper presents several relationships between the concept of associated random variables (RVs) and notions of stochastic ordering. The question that provides the impetus for this work is whether the association of the ℝ-valued RVs {X1,...,Xn} implies a possible stochastic ordering between the ℝn-valued RV X:¸=(X1,...,Xn) and its independent version nX:¸=(nX1,...,nXn). This leads to results on how multidimensional probability distributions are determined by conditions on their one-dimensional margin distributions in the event of comparison under the stochastic orderings ¸•st,¸•ci,¸•cv,¸•D and ¸•K. Such results have direct implications for the comparison of bounds for Fork-Join queues and for the structure of monotone functions of several variables.

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