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The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like 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 which 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

Institut d´Estadística de Catalunya (Idescat)

Author: Mateu i Figueras, Glòria
Pawlowsky-Glahn, Vera
Juan José, Egozcue
Date: 2014 March 27
Abstract: Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like 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 which 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
Document access: http://hdl.handle.net/2072/227384
Language: eng
Publisher: Institut d´Estadística de Catalunya (Idescat)
Rights: Attribution-NonCommercial-NoDerivs 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Subject: Distribució (Teoria de la probabilitat)
Distribution (Probability theory)
Title: The normal distribution in some constrained sample spaces
Type: info:eu-repo/semantics/article
Repository: Recercat

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