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Stochastically Monotone Dependence

Bennett Brady and Nozer D. Singpurwalla
Lecture Notes-Monograph Series
Vol. 16, Topics in Statistical Dependence (1990), pp. 93-102
Stable URL: http://www.jstor.org/stable/4355585
Page Count: 10
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Stochastically Monotone Dependence
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Abstract

The notion of monotone dependence, which has played a key role in reliability theory, is generalized to that of "stochastically monotone dependence." The idea here is that since two lifelengths are dependent or independent based on the disposition of a conditioning variable, they are unconditionally stochastically dependent or independent. A measure of stochastic dependence is introduced and the measure used for comparing the correlations of pairs of random variables which can now be described as being "highly stochastically correlated" or "weakly stochastically correlated." Extensions to the multivariate case are possible and the ideas illustrated via examples. This paper is expository; its purpose is to propose a natural idea and to explore its ramifications.

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