A new distribution on the simplex containing the Dirichlet family

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dc.contributor Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada
dc.contributor.author Ongaro, Andrea
dc.contributor.author Migliorati, Sonia
dc.contributor.author Monti, Gianna Serafina
dc.contributor.editor Daunis i Estadella, Josep
dc.contributor.editor Martín Fernández, Josep Antoni
dc.date.issued 2008-05-29
dc.identifier.citation Ongaro, A.; Migliorati, S.; Monti, G.S. 'A new distribution on the simplex containing the Dirichlet family' a CODAWORK’08. Girona: La Universitat, 2008 [consulta: 13 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/726
dc.identifier.uri http://hdl.handle.net/10256/726
dc.description.abstract The Dirichlet family owes its privileged status within simplex distributions to easyness of interpretation and good mathematical properties. In particular, we recall fundamental properties for the analysis of compositional data such as closure under amalgamation and subcomposition. From a probabilistic point of view, it is characterised (uniquely) by a variety of independence relationships which makes it indisputably the reference model for expressing the non trivial idea of substantial independence for compositions. Indeed, its well known inadequacy as a general model for compositional data stems from such an independence structure together with the poorness of its parametrisation. In this paper a new class of distributions (called Flexible Dirichlet) capable of handling various dependence structures and containing the Dirichlet as a special case is presented. The new model exhibits a considerably richer parametrisation which, for example, allows to model the means and (part of) the variance-covariance matrix separately. Moreover, such a model preserves some good mathematical properties of the Dirichlet, i.e. closure under amalgamation and subcomposition with new parameters simply related to the parent composition parameters. Furthermore, the joint and conditional distributions of subcompositions and relative totals can be expressed as simple mixtures of two Flexible Dirichlet distributions. The basis generating the Flexible Dirichlet, though keeping compositional invariance, shows a dependence structure which allows various forms of partitional dependence to be contemplated by the model (e.g. non-neutrality, subcompositional dependence and subcompositional non-invariance), independence cases being identified by suitable parameter configurations. In particular, within this model substantial independence among subsets of components of the composition naturally occurs when the subsets have a Dirichlet distribution
dc.description.sponsorship Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
dc.rights Tots els drets reservats
dc.subject Invariància
dc.subject Models matemàtics
dc.subject Dirichlet, Principi de
dc.subject Dirichlet, Distribució de
dc.subject Dirichlet distribution
dc.title A new distribution on the simplex containing the Dirichlet family
dc.type info:eu-repo/semantics/conferenceObject

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