Displaying similar documents to “Properties of the induced semigroup of an Archimedean copula”

Characterizations of Archimedean n -copulas

Włodzimierz Wysocki (2015)

Kybernetika

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We present three characterizations of n -dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n -variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by...

Non-Archimedean K-spaces

Albert Kubzdela (2005)

Banach Center Publications

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We study Banach spaces over a non-spherically complete non-Archimedean valued field K. We prove that a non-Archimedean Banach space over K which contains a linearly homeomorphic copy of l ∞ (hence l ∞ itself) is not a K-space. We discuss the three-space problem for a few properties of non-Archimedean Banach spaces.

A new family of trivariate proper quasi-copulas

Manuel Úbeda-Flores (2007)

Kybernetika

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In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that W 3 – the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) – is the limit member of this family, showing how the mass of W 3 is distributed on the plane x + y + z = 2 of [ 0 , 1 ] 3 in an easy manner, and providing the generalization of this result to n dimensions.

Asymmetric semilinear copulas

Bernard De Baets, Hans De Meyer, Radko Mesiar (2007)

Kybernetika

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We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1 / 16 . The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π and M .

Random noise and perturbation of copulas

Radko Mesiar, Ayyub Sheikhi, Magda Komorníková (2019)

Kybernetika

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For a random vector ( X , Y ) characterized by a copula C X , Y we study its perturbation C X + Z , Y characterizing the random vector ( X + Z , Y ) affected by a noise Z independent of both X and Y . Several examples are added, including a new comprehensive parametric copula family 𝒞 k k ∈ [ - ∞ , ∞ ] .

On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar (2022)

Kybernetika

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Assuming that C X , Y is the copula function of X and Y with marginal distribution functions F X ( x ) and F Y ( y ) , in this work we study the selection distribution Z = d ( X | Y ∈ T ) . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.

Approximate polynomial expansion for joint density

D. Pommeret (2005)

Applicationes Mathematicae

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Let (X,Y) be a random vector with joint probability measure σ and with margins μ and ν. Let ( P ₙ ) n ∈ ℕ and ( Q ₙ ) n ∈ ℕ be two bases of complete orthonormal polynomials with respect to μ and ν, respectively. Under integrability conditions we have the following polynomial expansion: σ ( d x , d y ) = ∑ n , k ∈ ℕ ϱ n , k P ₙ ( x ) Q k ( y ) μ ( d x ) ν ( d y ) . In this paper we consider the problem of changing the margin μ into μ̃ in this expansion. That is the case when μ is the true (or estimated) margin and μ̃ is its approximation. It is shown that a new joint probability with...