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 evaluation, this ebook can bestrongly steered to probabilists and statisticians who deal withdistributions with given marginals.
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Extra resources for Advances in Probability Distributions with Given Marginals: Beyond the Copulas

Example text

1L__. . ( O . O . 1. 1. 8) If H is continuous, then C is unique; otherwise C is uniquely de- termined on the Cartesian product (Ran Fl)X (RanF 2 )X •.. x(RanF n ). •• ,F n . Thus copulas are the functions that link n-dimensional distribution functions to their one-dimensional margins. i = l, ... ,n, Moreover, letting u. = F. ), 111 yields (1. 8), shows that much of the study of joint distribution functions can be reduced to the study of copulas. 9) induces an equivalence relation on the space of n-dimensional distribution functions, where two such functions are equivalent (belong to the same Frechet class) if and only if they determine the same copula.

The contribution of V. Bene~ and J. ~t~pan to this volume). Recently, Sherwood and Taylor [67] came to this problem from a different direction. Motivated by the idea of redistributing the mass of Min from the main diagonal of the unit square onto two curves joining the corners (0,0) and (1,1), they defined a hairpin as the graph of g u g -1 , where creasing homeomorphism of the unit interval satisfying ° for < U < 1 and g-l is the inverse of g. g ° is an in< g(u) < u Then, using an ap- proach that employs functional equations, they found necessary conditions and sufficient conditions on g for the hairpin g u g contain the support of a doubly stochastic measure (copula).

0). 1). 1L__. . ( O . O . 1. 1. 8) If H is continuous, then C is unique; otherwise C is uniquely de- termined on the Cartesian product (Ran Fl)X (RanF 2 )X •.. x(RanF n ). •• ,F n . Thus copulas are the functions that link n-dimensional distribution functions to their one-dimensional margins. i = l, ... ,n, Moreover, letting u. = F. ), 111 yields (1. 8), shows that much of the study of joint distribution functions can be reduced to the study of copulas. 9) induces an equivalence relation on the space of n-dimensional distribution functions, where two such functions are equivalent (belong to the same Frechet class) if and only if they determine the same copula.

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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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