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The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach

The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used to look at the Dirichlet family of distributions from a new perspective. A classical Dirichlet density function is expressed with respect to the Lebesgue measure on real space. We propose here to change this measure by the Aitchison measure on the simplex, and study some properties and characteristic measures of the resulting density

Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i Tecnología.

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Manager: Mateu i Figueras, Glòria
Barceló i Vidal, Carles
Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Mateu i Figueras, Glòria
Pawlowsky-Glahn, Vera
Date: 2005 October
Abstract: The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used to look at the Dirichlet family of distributions from a new perspective. A classical Dirichlet density function is expressed with respect to the Lebesgue measure on real space. We propose here to change this measure by the Aitchison measure on the simplex, and study some properties and characteristic measures of the resulting density
Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i Tecnología.
Format: application/pdf
Citation: Mateu i Figueras, G.; Pawlowsky Glahn, V. ’The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach’ a CODAWORK’05. Girona: La Universitat, 2005 [consulta: 5 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/666
Document access: http://hdl.handle.net/10256/666
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Collection: info:eu-repo/semantics/altIdentifier/isbn/84-8458-222-1
Rights: Tots els drets reservats
Subject: Aitchison, Geometria d’
Propietat de Radon-Nikodym
Pertorbació (Matemàtica)
Dirichlet, Distribució de
Dirichlet distribution
Title: The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach
Type: info:eu-repo/semantics/conferenceObject
Repository: DUGiDocs

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