Download PDF by G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti: Advances in Probability Distributions with Given Marginals:

By G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)

ISBN-10: 9401055343

ISBN-13: 9789401055345

ISBN-10: 9401134669

ISBN-13: 9789401134668

As the reader could most likely already finish from theenthusiastic phrases within the first traces of this overview, this e-book can bestrongly advised to probabilists and statisticians who deal withdistributions with given marginals.
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Additional info for Advances in Probability Distributions with Given Marginals: Beyond the Copulas

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83, 834-841. Menger, K. (1942) Statistical metrics, Proc. Nat. Acad. Sci. A. 28, 535-537. Moore, D. S. and Spruill, M. C. (1975) Unified large-sample theory of general chi-squared statistics for tests of fit, Ann. of Math. 65, 117-143. Mostert, P. S. and Shields. A. L. (1957) On the structure of semigroups on a compact manifold with boundary, Ann. Statist. 3, 599-616. Moynihan, R. (1978) On TT-semigroups of probability distribution 29. 30.

2d). Accordingly, in the years 1961-63, Sklar and I turned our attention to this functional equation [60]. v)e learned that it has a long and distinguished history dating back to Abel and 21 THIRTY YEARS OF COPULAS became aware of the important results due to J. Aczel [1] (see also [2] and [62, Chapter 5]). 1. These yielded the following: Let T be a t-norm which is continuous on [0,1]2 2 and strictly increasing on (0,1] . 1) where the one-place function on [0,1], with tion of f. 1) is a continuous t-norm.

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.

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Advances in Probability Distributions with Given Marginals: Beyond the Copulas by G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)


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