A general theory of some positive dependence notions

Moshe Shaked

Journal of Multivariate Analysis, 1982, vol. 12, issue 2, 199-218

Abstract: A general theory of concepts of positive dependence, which are weaker than association but stronger than orthant dependence, is developed. A random vector X is associated if and only if P(X [set membership, variant] A [down curve] B) >= P(X [set membership, variant] A) P(X [set membership, variant] B) for all open upper sets A and B. By requiring the above inequality to hold only for some open upper sets A and B various notions of positive dependence which are weaker than association are obtained. First a general theory is given and then the results are specialized to some concepts of a particular interest. Various properties and interrelationships are derived and some applications are discussed.

Keywords: Positive; dependence; association; orthant; dependence; upper; sets; stachastic; ordering; reliability; theory; coherent; life; functions; exponential; minimums; invariance; principle; probability; inequalities (search for similar items in EconPapers)
Date: 1982
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Citations: View citations in EconPapers (15)

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