Hilbert space on probability density functions with Aitchison geometry
dc.contributor
dc.contributor.author
dc.date.accessioned
2008-05-02T10:15:02Z
dc.date.available
2008-05-02T10:15:02Z
dc.date.issued
2003-10-15
dc.identifier.citation
Egozcue, J.J.; Díaz Barrero, J.L. 'Hilbert space on probability density functions with Aitchison geometry' a CODAWORK’03. Girona: La Universitat, 2003 [consulta: 2 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/649
dc.identifier.isbn
84-8458-111-X
dc.identifier.uri
dc.description.abstract
Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities
by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities
dc.description.sponsorship
Geologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; 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.
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
dc.title
Hilbert space on probability density functions with Aitchison geometry
dc.type
info:eu-repo/semantics/conferenceObject
dc.rights.accessRights
info:eu-repo/semantics/openAccess