By G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)
As the reader might most likely already finish from theenthusiastic phrases within the first strains of this overview, this publication can bestrongly suggested to probabilists and statisticians who deal withdistributions with given marginals.
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Extra info for Advances in Probability Distributions with Given Marginals: Beyond the Copulas
Statist. Math. 39, 113-128. Kimeldorf, G. and Sampson, A. R. (1989) A framework for positive dependence, Ann. Inst. Statist. Math. 41, 31-45. Kotz, S. and Johnson, N. L. (1977) Proprietes de dependance des distributions interees generalisees deux variables FarlieGumbel-Morgenstern, C. R. Acad. Sci. Paris 285A, 277-280. Kruskal, W. H. (1958) Ordinal measures of association, J. Amer. Statist. Assoc. 53, 814-861. Lehmann, E. L. (1966) Some concepts of dependence, Ann. Math. Statist. 37, 1137-1153.
To make this more precise, we need the following: Generally 28 B. 1. f. 's defined on a common probability space, such that df(X) = F, =G df(Y) and df(V(X,Y)) = ~(F,G). 1. Min. Then 'T Let T be any (left-continuous) t-norm other than is not derivable from any function on random variables. 6) below. 1) F pr Fpq * q p,q,r lies between of a probabilistic metric p and r if and only if Fqr , and he showed that this relation has all the properties of ordinary metric betweenness. 2) F = ,(F ,F ). pr pq qr is Wald-between p and r if and only if But now the situation is more complicated since an arbitrary triangle function may not possess all the pleasant properties of convolution.
In but it is not hard to V. MEASURES OF DEPENDENCE The results presented in the first part of this paper were all ob- tained in connection with and as offshoots of problems arising in the theory of probabilistic metric spaces. Those of us working on these matters had no formal training in statistics. Thus we were only tan- gentially aware of possible statistical applications. Moreover, with the notable exception of Sklar's original paper , our results were presented in a novel context and published in journals not generally read by statisticians.