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Characterizacion of the bivariate discrete distributions defined by a partial difference equations system.

Ramón Gutiérrez Jáimez, Miguel Angel Fajardo Caldera (1988)

Trabajos de Estadística

Conditions under which the solutions of a partial difference equations system can be probability functions are examined.When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.

Characterization of lung tumor subtypes through gene expression cluster validity assessment

Giorgio Valentini, Francesca Ruffino (2006)

RAIRO - Theoretical Informatics and Applications

The problem of assessing the reliability of clusters patients identified by clustering algorithms is crucial to estimate the significance of subclasses of diseases detectable at bio-molecular level, and more in general to support bio-medical discovery of patterns in gene expression data. In this paper we present an experimental analysis of the reliability of clusters discovered in lung tumor patients using DNA microarray data. In particular we investigate if subclasses of lung adenocarcinoma...

Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values

Wiktor Oktaba (1998)

Applications of Mathematics

The aim of this paper is to characterize the Multivariate Gauss-Markoff model ( M G M ) as in () with singular covariance matrix and missing values. M G M D P 2 model and completed M G M D P 2 Q model are obtained by three transformations D , P and Q (cf. ()) of M G M . The unified theory of estimation (Rao, 1973) which is of interest with respect to M G M has been used. The characterization is reached by estimation of parameters: scalar σ 2 and linear combination λ ' B ¯ ( B ¯ = v e c B ) as in (), (), () as well as by the model of the form () (cf. Th. )....

Characterizations of Archimedean n -copulas

Włodzimierz Wysocki (2015)

Kybernetika

We present three characterizations of n -dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n -variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by means of an...

Characterizing experimental designs by properties of the standard quadratic forms of observations

Czesław Stępniak (2007)

Applicationes Mathematicae

For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.

Classification croisée et modèles

Y. Bencheikh (2010)

RAIRO - Operations Research

The relations between automatic clustering methods and inferentiel statistical models have mostely been studied when the data involves only one set. We propose to study these relations in the case of data involving two sets. We shall look at cross clustering methods as suggested by Govaert [6]; we show that these methods, like the simple clustering methods, can be considered as a clustering approach of a mixture model. We introduce the notion of crossed mixture from a concret example and...

Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution

Ewa Świercz (2010)

International Journal of Applied Mathematics and Computer Science

A new supervised classification algorithm of a heavily distorted pattern (shape) obtained from noisy observations of nonstationary signals is proposed in the paper. Based on the Gabor transform of 1-D non-stationary signals, 2-D shapes of signals are formulated and the classification formula is developed using the pattern matching idea, which is the simplest case of a pattern recognition task. In the pattern matching problem, where a set of known patterns creates predefined classes, classification...

Classification into two von Mises distributions with unknown mean directions

Kryštof Eben (1983)

Aplikace matematiky

The paper deals with two Mises distributions on the circle with unknown mean directions and a common concentration parameter that is known. The likelihood rule and the plug-in rule are examined. For the statistic of the plug-in rule, the moment generating function is given and a method of obtaining the moments is proposed.

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