The importance of being the upper bound in the bivariate family

Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric prior distribution which puts mass on the null hypothesis. Accepting this hypothesis is equivalent to reaching the upper bound. We also present some parametric families making emphasis on this bound

Geometrical understanding of the Cauchy distribution

Advanced calculus is necessary to prove rigorously the main properties of the Cauchy distribution. It is well known that the Cauchy distribution can be generated by a tangent transformation of the uniform distribution. By interpreting this transformation on a circle, it is possible to present elementary and intuitive proofs of some important and useful properties of the distributio

Estadística, societat i veritat

Se hace una exposición general de la incidencia de la estadística en la sociedad, desde una perspectiva histórica y actual. Los métodos y resultados de la estadística representan una forma actual e imprescindible del pensamiento, que abarca todos los campos del conocimiento y todas las actividades humanas

La producció científica dels darrers onze anys de Qüestiió

Peer Reviewe

Geometrical understanding of the Cauchy distribution

Advanced calculus is necessary to prove rigorously the main properties of the Cauchy distribution. It is well known that the Cauchy distribution can be generated by a tangent transformation of the uniform distribution. By interpreting this transformation on a circle, it is possible to present elementary and intuitive proofs of some important and useful properties of the distribution

The importance of being the upper bound in the bivariate family.

Any bivariate cdf is bounded by the Fr ´echet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric prior distribution which puts mass on the null hypothesis. Accepting this hypothesis is equivalent to reaching the upper bound. We also present some parametric families making emphasis on this bound

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum

El llegat de Galton, Pearson Fréchet i d'altres: com mesurar i interpretar l'associació estadística

Presentem en tres parts els conceptes de correlació i d'associació estadística, començant per la noció de correlació de Galton, millorada per Pearson. Utilitzem com a il. lustració les dades clàssiques de Galton i Pearson sobre heretabilitat de pares i fills respecte a l'estatura. La segona part explica com s'han d'estudiar les mateixes dades des d'una perspectiva multivariant (anàlisi de correlació canònica i de correspondències). Utilitzem també dades de Fisher. Mostrem com podem associar dades de tipus general mitjançant distàncies. La tercera part la dediquem a les distribucions bivariants. Presentem la teoria de funcions i valors propis per a dos nuclis, que s'aplica al desenvolupament diagonal d'una distribució bivariant, incloent-hi els desenvolupaments continus en termes d'integrals. Proposem una família de còpules canòniques, que permet generar distribucions bivariants

Una contribución al análisis de proximidades

Una contribución al análisis de proximidade

Aplicación del análisis canónico al estudio de la mineralización del yacimiento de Osor (Girona)

El análisis canónico de la mineralización de Osor se ha efectuado con 78 muestras de 7 variables (la cantidad en ppm de los elementos menores siguientes: Ba, Y, Fe, Zn, Cu, Mn, Si). Ha permitido establecer: 1) la mineralización en apariencia homogénea, presenta zonas de génesis diferentes ; 2) en cada filón las condiciones de deposición varían con la profundidad; 3) ,dos filones, aparentemente iguales, muestran diferentes procesos genéticos