On a conditional Cauchy functional equation of several variables and a characterization of multivariate stable distributions.
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Displaying 1 – 20 of 26
On a probability inequality for multivariate normal distribution
Somesh Das Gupta (1976)
Aplikace matematiky
On a problem by Schweizer and Sklar
Fabrizio Durante (2012)
Kybernetika
We give a representation of the class of all -dimensional copulas such that, for a fixed , , all their -dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.
On asymmetric distributions of copula related random variables which includes the skew-normal ones
Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar (2022)
Kybernetika
Assuming that is the copula function of and with marginal distribution functions and , in this work we study the selection distribution . 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.
On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators
Elena Di Bernardino, Didier Rullière (2013)
Dependence Modeling
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these...
On concordance measures for discrete data and dependence properties of Poisson model.
Bouezmarni, Taoufik, Mesfioui, Mhamed, Tajar, Abdelouahid (2009)
Journal of Probability and Statistics
On conditional independence and log-convexity
František Matúš (2012)
Annales de l'I.H.P. Probabilités et statistiques
If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.
On Conditional Value at Risk (CoVaR) for tail-dependent copulas
Piotr Jaworski (2017)
Dependence Modeling
The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.
On copulas that generalize semilinear copulas
Juan Fernández Sánchez, Manuel Úbeda-Flores (2012)
Kybernetika
We study a wide class of copulas which generalizes well-known families of copulas, such as the semilinear copulas. We also study corresponding results for the case of quasi-copulas.
On distributions of order statistics for absolutely continuous copulas with applications to reliability
Piotr Jaworski, Tomasz Rychlik (2008)
Kybernetika
Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous...
On generalized conditional cumulative past inaccuracy measure
Amit Ghosh, Chanchal Kundu (2018)
Applications of Mathematics
The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI...
On independence in some families of multivariate distributions.
José Juan Quesada (1986)
Stochastica
In this paper we will prove a characterization for the independence of random vectors with positive (negative) orthant dependence according to a direction. The result can be seen as a generalization of a result by Lehmann [4].
On monotone dependence functions of the quantile type
Andrzej Krajka, Dominik Szynal (1995)
Applicationes Mathematicae
We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.
On probabilities in certain multivariate distributions: their dependence on correlations
Zbyněk Šidák (1973)
Aplikace matematiky
On quasi-homogeneous copulas
Gaspar Mayor, Radko Mesiar, Joan Torrens (2008)
Kybernetika
Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.
On structural approximating multivariate discrete probability distributions
Jiří Grim (1984)
Kybernetika
On the connection between cherry-tree copulas and truncated R-vine copulas
Edith Kovács, Tamás Szántai (2017)
Kybernetika
Vine copulas are a flexible way for modeling dependences using only pair-copulas as building blocks. However if the number of variables grows the problem gets fastly intractable. For dealing with this problem Brechmann at al. proposed the truncated R-vine copulas. The truncated R-vine copula has the very useful property that it can be constructed by using only pair-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this...
On the Jensen-Shannon divergence and the variation distance for categorical probability distributions
Jukka Corander, Ulpu Remes, Timo Koski (2021)
Kybernetika
We establish a decomposition of the Jensen-Shannon divergence into a linear combination of a scaled Jeffreys' divergence and a reversed Jensen-Shannon divergence. Upper and lower bounds for the Jensen-Shannon divergence are then found in terms of the squared (total) variation distance. The derivations rely upon the Pinsker inequality and the reverse Pinsker inequality. We use these bounds to prove the asymptotic equivalence of the maximum likelihood estimate and minimum Jensen-Shannon divergence...
On the moments of random variables uniformly distributed over a polytope.
Paramasamy, S. (1997)
International Journal of Mathematics and Mathematical Sciences
On the multivariate skew-normal distribution and its scale mixtures.
Vernic, Raluca (2005)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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