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

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 ebook can bestrongly steered to probabilists and statisticians who deal withdistributions with given marginals.
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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.

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