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Sample d -copula of order m

José M. González-Barrios, María M. Hernández-Cedillo (2013)

Kybernetika

In this paper we analyze the construction of d -copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample d -copula of order m with m 2 , the central idea is to use the above methodologies to construct a new copula based on a sample. The...

Semicopulæ

Fabrizio Durante, Carlo Sempi (2005)

Kybernetika

We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, t -norm.

Semicopulas: characterizations and applicability

Fabrizio Durante, José Quesada-Molina, Carlo Sempi (2006)

Kybernetika

We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.

Sets of determination for parabolic functions on a half-space

Jarmila Ranošová (1994)

Commentationes Mathematicae Universitatis Carolinae

We characterize all subsets M of n × + such that sup X n × + u ( X ) = sup X M u ( X ) for every bounded parabolic function u on n × + . The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of M is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated.

Shuffles of Min.

Piotr Mikusinski, Howard Sherwood, Michael D. Taylor (1992)

Stochastica

Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which...

Small perturbations with large effects on value-at-risk

Manuel L. Esquível, Luís Dimas, João Tiago Mexia, Philippe Didier (2013)

Discussiones Mathematicae Probability and Statistics

We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.

Some properties of the proportional odds model

Magdalena Benduch-Frąszczak (2010)

Applicationes Mathematicae

Marshall and Olkin (1997) introduced a new family of distributions by adding a tilt parameter. The same family was obtained by Kirmani and Gupta (2001) as the proportional odds model, which had been proposed by Clayton (1974). In this paper, stochastic ordering of distributions from this class and preservation of classes of life distributions by adding a parameter are obtained. The proportional odds family is also considered as a family of weighted distributions.

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