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Petr Kratochvíl (1990)
Aplikace matematiky
The author shows that a decomposition of a covariance matrix implies the corresponding model, i.e. the existence of factors such that is true. The result is applied to the general linear model of factor analysis. A procedure for computing the factor score is proposed.
Daniel Hlubinka, Samuel Kotz (2010)
Applications of Mathematics
The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.
Bartosz Kołodziejek (2013)
Studia Mathematica
We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Wesołowski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.
Konstancja Bobecka, Jacek Wesołowski (2002)
Studia Mathematica
The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental reason...
Janos Galambos (1982)
Aequationes mathematicae
Kovacs, Edith (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
Erich Peter Klement, Radko Mesiar, Endre Pap (2005)
Kybernetika
Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.
Milan Studený, Alberto Roverato, Šárka Štěpánová (2009)
Kybernetika
In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use...
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