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

*As the reader might most likely already finish from the**enthusiastic phrases within the first strains of this overview, this ebook can be**strongly steered to probabilists and statisticians who deal with**distributions with given marginals.***Mededelingen van het Wiskundig Genootschap**

**Read Online or Download Advances in Probability Distributions with Given Marginals: Beyond the Copulas PDF**

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**Additional info for Advances in Probability Distributions with Given Marginals: Beyond the Copulas**

**Example text**

Any measure of dis- = xy will be a measure of dependence between pairs of random variables Whose copula is first measure that came to mind was the C. 1) for any pair of random variables X and Y. I worked out some of its properties and showed that, in essence, it satisfied most of Renyi's conditions. F. Wolff and we began to work on them together. This led to a preliminary an- nouncement published in 1976 [63], to Holff's doctoral dissertation [79] a year later, and to a joint paper Which appeared in the Annals of Statistics in 1981 [64].

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.

Menger in 1942 [44]. As defined in the 1958 Comptes Rendus note with Sklar, a probabilistic metric space is an ordered pair and F is a mapping from S x S (S,F), into the space t:,,+ where is a set S of probability dis- . 1) on (_00,00), nondecreasing, and For any pair of points p, q in S is left-continuous F(O) =0, F(oo) = 1}. the distribution function F(p,q) is generally denoted by F and, for any real x, its value F (x) is usupq pq ally interpreted as the probability that the "distance" between p and q is less than (I) F (II) F pq pq The distribution functions x.