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Concepts of dependence and stochastic ordering for bivariate distributions. (Concepts de dépendance et ordres stochastiques pour des lois bidimensionelles.) (French) Zbl 0738.62057
Summary: T. Yanagimoto and M. Okamoto [Ann. Inst. Stat. Math. 21, 489–506 (1969; Zbl 0208.44704)] introduced a stochastic ordering that generalizes a concept of monotone regression dependence introduced by E. L. Lehmann [Ann. Math. Stat. 37, 1137–1153 (1966; Zbl 0146.40601)]. We define and examine the properties of three new orderings which imply that of Yanagimoto and Okamoto. One of these orderings is seen to extend M. Shaked’s [J. Am. Stat. Assoc. 72, 642–650 (1977; Zbl 0375.62092)] notion of \(DTP(0,1)\), and another includes Lehmann’s concept of positive likelihood-ratio dependence as a special case. The proposed orderings are also compared with the \(TP_2\) positive-dependence ordering defined by G. Kimeldorf and A. R. Sampson [Ann. Inst. Stat. Math. 39, 113–128 (1987; Zbl 0617.62006)].

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
60E15 Inequalities; stochastic orderings
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