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Defects and transformations of quasi-copulas

Michal Dibala, Susanne Saminger-Platz, Radko Mesiar, Erich Peter Klement (2016)

Kybernetika

Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being...

Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

The following three results for the general multivariate Gauss-Markoff model with a singular covariance matrix are given or indicated. 1 ∘ determinant ratios as products of independent chi-square distributions, 2 ∘ moments for the determinants and 3 ∘ the method of obtaining approximate densities of the determinants.

Detection of influential points by convex hull volume minimization

Petr Tichavský, Pavel Boček (1998)

Kybernetika

A method of geometrical characterization of multidimensional data sets, including construction of the convex hull of the data and calculation of the volume of the convex hull, is described. This technique, together with the concept of minimum convex hull volume, can be used for detection of influential points or outliers in multiple linear regression. An approximation to the true concept is achieved by ordering the data into a linear sequence such that the volume of the convex hull of the first...

Discrete generalized Liouville-type distribution and related multivariate distributions.

G. S. Lingappaiah (1984)

Trabajos de Estadística e Investigación Operativa

Discrete analogue of the Liouville distribution is defined and is termed as Discrete Generalized Liouville-Type Distribution (DGL-TD). Firstly, properties in its factorial and ordinary moments are given. Then by finding the covariance matrix, partial and multiple correlations for DGL-TD are evaluated. Multinomial, multivariate negative binomial and multivariate log series distributions are shown as particular cases of this general distribution. The asymptotic distribution of the estimates of the...

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