By G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)
As the reader may most likely already finish from theenthusiastic phrases within the first traces of this assessment, this ebook can bestrongly instructed 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
And Rivest, L. P. (1989) A characterization of Gumbel's family of extreme value distributions, Statist. and Probab. Letters 8, 207-211. a 48 B. SCHWEIZER 27. Hoeffding, W. (1940) Masstabinvariante Korrelationstheorie, Schrif- 28. , Sherwood, H. and Taylor, M. D. (1988) Properties of a special class of doubly stochastic measures, Aequationes Math. 36, 212-229. Kellerer, H. G. (1964) Masstheoretische Marginalprobleme, Math. Ann. 153, 168-198. Kellerer, H. (1964) Verteilungsfunktionen mit gegebenen Harginalverteilungen, Z.
8. WHEN MARGINS ARE FIXED By now the reader should be aware of the fact that any paper bear- ing a title that contains a phrase such as "when the margins are fixed" is a paper involving copulas. More often than not (since copulas are not yet as well-known as they might be) this involvement is implicit. Consequently, there is generally something to be gained - insight at the very least - by bringing the role of copulas explicitly to the fore. To illustrate, in 1983, while browsing through the Mathematical Reviews, 40 B.
5) W(a,b) Note that Both Z W defined on = = and [0,1]2 Z and (0,1,0) and above by the graph of Min are t-norms, as are the funcby ab, Max(a + b - 1,0). W, Prod and Min are copulas as well as t-norms. 2c) are natural requirements and have ready interpretations. 2d), which was first in- troduced in , is needed in order to extend Menger's triangle inequality to a polygonal inequality. Soon after the appearance of Menger's paper, A. 6) where Fpr => Fpq * * For all p,q,r in S, F qr denotes convolution.
Advances in Probability Distributions with Given Marginals: Beyond the Copulas by G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)