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Daunis i Estadella, Josep
MartÃn FernÃ¡ndez, Josep Antoni 

Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tolosana Delgado, Raimon
Boogaart, K. Gerald van den Mikes, TÃ¼nde Eynatten, Hilmar von 

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and DÂ´Ä±azBarrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermitepolynomialsbased basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all korder polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2order Hermite polinomials (normal reference)and 1order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition Geologische Vereinigung; Institut dâ€™EstadÃstica de Catalunya; International Association for Mathematical Geology; CÃ tedra LluÃs SantalÃ³ dâ€™Aplicacions de la MatemÃ tica; Generalitat de Catalunya, Departament dâ€™InnovaciÃ³, Universitats i Recerca; Ministerio de EducaciÃ³n y Ciencia; Ingenio 2010. 

http://hdl.handle.net/2072/14764  
eng  
Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tots els drets reservats  
Probabilitats
EstadÃstica matemÃ tica 

Statistical treatment of grainsize curves and empirical distributions: densities as compositions?  
info:eurepo/semantics/conferenceObject  
Recercat 