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Title:	The normal distribution in some constrained sample spaces
Author:	Mateu Figueras, Gloria; Pawlowsky Glahn, Vera; Egozcue Rubí, Juan José
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística
Abstract:	Phenomena with a constrained sample space appear frequently in practice. This is the case, for example, with strictly positive data, or with compositional data, such as percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models that better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat -Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica -Probabilities -Distribution (Probability theory) -Additive logistic normal distribution -Aitchison measure -Lebesgue measure -lognormal distribution -orthonornnal basis -simplex -COMPOSITIONAL DATA-ANALYSIS -SKEW-NORMAL DISTRIBUTION -STATISTICAL-ANALYSIS -SIMPLEX -Probabilitats -Distribució (Teoria de la probabilitat) -60A Foundations of probability theory -62E Distribution theory
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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