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Download Copula Theory and Its Applications: Proceedings of the by Piotr Jaworski PDF

By Piotr Jaworski

Copulas are mathematical items that totally catch the dependence constitution between random variables and consequently supply nice flexibility in construction multivariate stochastic versions. considering that their advent within the early 50's, copulas have won significant attractiveness in different fields of utilized arithmetic, comparable to finance, coverage and reliability idea. this day, they signify a well-known device for industry and credits versions, aggregation of dangers, portfolio choice, and so on. This ebook is split into major elements: half I - "Surveys" includes eleven chapters that offer an up to date account of crucial facets of copula types. half II - "Contributions" collects the prolonged models of 6 talks chosen from papers awarded on the workshop in Warsaw.

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Additional info for Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25-26 September 2009

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2, are usually called meta-elliptical distribution [63]. 1. Let X be an elliptical random vector, X ∼ Ed (μ , Σ , g). Suppose √ that, for every i ∈ {1, 2, . . , d}, (Xi / σii ) ∼ Fg . We call elliptical copula the distribution function of the random vector X1 √ σ11 Fg , Fg X2 √ σ22 Xd √ σdd , . . , Fg . An elliptical copula is typically not available in closed form. In order just to provide an example, the bivariate Gaussian copula is given by Cθ (u1 , u2 ) = Φ −1 (u1 ) −∞ Φ −1 (u2 ) −∞ 1 √ 2π 1 − θ 2 − s2 − 2θ st + s2 2(1 − θ 2 ) dsdt, where θ ∈ [−1, 1], and Φ −1 denotes the inverse of the univariate Gaussian distribution.

Plan. Infer. 139(11), 3921–3927 (2009) 176. , Taylor, M. ): Distributions with Fixed Marginals and Related Topics. Institute of Mathematical Statistics Lecture Notes—Monograph Series, vol. 28. Institute of Mathematical Statistics, Hayward, CA (1996) 177. : Extremes in Nature. An Approach Using Copulas. Water Science and Technology Library, vol. 56. Springer, Dordrecht (NL) (2007) 1 Copula Theory: An Introduction 31 178. : Generalized normal correlation and two-dimensional Fréchet classes. Dokl.

Essentially, three kinds of such constructions can be distinguished. 1 Copulas with Given Lower Dimensional Marginals These constructions are strictly related to the original Fréchet problem of considering distribution functions with fixed marginals (eventually overlapping). In this context the most interesting results have been obtained by means of the “conditioning method”, as used by Dall’Aglio [29, 30] and Rüschendorf [174]. Joe presented several results of this type in [104, Chap. 3]. A powerful recent method based on these ideas is the so-called pair-copula construction (for more details, see [28] and the references therein).

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