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The normal distribution in some constrained sample spaces
Mateu Figueras, Gloria; Pawlowsky Glahn, Vera; Egozcue Rubí, Juan José
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística
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.
Peer Reviewed
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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