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 could most likely already finish from theenthusiastic phrases within the first strains of this evaluation, this booklet can bestrongly prompt 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
S. s. strictly increasing transformations. 1 and 000 02 satisfies conditions (A) - (H) of The- satisfies all but condition (E). 7) q, is given by q(X,Y) = 4C xy (1/2,1/2) - 1. 7) extend to higher dimensions. In , Wolff introduced higher dimensional analogues of the modified Renyi conditions (A) - (H) and studied the n-dimensional versions of 0, p, and T in this light. 6) is not a copula and the graph of Prod n lies much closer to the graph of Wn than to the graph of Minn. 34 7. B. SCHWEIZER CONNECTIONS While Wolff was working on his dissertation , and later in the course of writing our joint paper , we became aware of the extensive literature related, directly and indirectly, to copulas and the role copulas play in questions of dependence.
Soon after the appearance of Menger's paper, A. 6) where Fpr => Fpq * * For all p,q,r in S, F qr denotes convolution. 6) is too stringent. 3. 2d). Accordingly, in the years 1961-63, Sklar and I turned our attention to this functional equation . 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  (see also  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] .
Responded with an enthusiastic "Yes"; I and, presumptuously assuming that I would be invited to speak, began to think about a possible topic. An historical survey seemed appropriate and the first title that came to mind was "Copulas and their uses". I soon realized that this was far too ambitious an undertaking and therefore decided to limit my scope, to stay with what I knew best, and to describe my personal involvement with the subject over a span of three decades. That was the substance of my talk in Rome and that, in expanded form, is also the essence of this paper.