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On computations with causal compositional models

Vladislav Bína, Radim Jiroušek (2015)

Kybernetika

The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl's causality approach. The paper brings an alternative, purely algebraic methodology...

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 eliminating transformations for nuisance parameters in multivariate linear model

Pavla Kunderová (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered. We examine eliminating transformations which eliminate the nuisance parameters without loss of information on the useful parameters and on the variance components.

On extremal dependence of block vectors

Helena Ferreira, Marta Ferreira (2012)

Kybernetika

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to...

On factorization of probability distributions over directed graphs

František Matúš, Bernhard Strohmeier (1998)

Kybernetika

Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple,...

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 α 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 geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters

Konrad Neumann, Stefan Zontek (2006)

Discussiones Mathematicae Probability and Statistics

We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of...

On identifiability of mixtures of independent distribution laws

Mikhail Kovtun, Igor Akushevich, Anatoliy Yashin (2014)

ESAIM: Probability and Statistics

We consider representations of a joint distribution law of a family of categorical random variables (i.e., a multivariate categorical variable) as a mixture of independent distribution laws (i.e. distribution laws according to which random variables are mutually independent). For infinite families of random variables, we describe a class of mixtures with identifiable mixing measure. This class is interesting from a practical point of view as well, as its structure clarifies principles of selecting...

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