The normal distribution in some constrained sample spaces

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...

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Autores: Mateu Figueras, Gloria, Pawlowsky Glahn, Vera, Egozcue Rubí, Juan José|||0000-0002-5144-4483
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/23204
Acceso en línea:https://hdl.handle.net/2117/23204
Access Level:acceso abierto
Palabra clave: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
Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
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spelling The normal distribution in some constrained sample spacesMateu Figueras, GloriaPawlowsky Glahn, VeraEgozcue Rubí, Juan José|||0000-0002-5144-4483ProbabilitiesDistribution (Probability theory)Additive logistic normal distributionAitchison measureLebesgue measurelognormal distributionorthonornnal basissimplexCOMPOSITIONAL DATA-ANALYSISSKEW-NORMAL DISTRIBUTIONSTATISTICAL-ANALYSISSIMPLEXProbabilitatsDistribució (Teoria de la probabilitat)60A Foundations of probability theory62E Distribution theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::ProbabilitatÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàticaPhenomena 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 Reviewed20132013-01-0120142014-06-12journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/23204reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/232042026-05-27T15:37:01Z
dc.title.none.fl_str_mv The normal distribution in some constrained sample spaces
title The normal distribution in some constrained sample spaces
spellingShingle The normal distribution in some constrained sample spaces
Mateu Figueras, Gloria
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
Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
title_short The normal distribution in some constrained sample spaces
title_full The normal distribution in some constrained sample spaces
title_fullStr The normal distribution in some constrained sample spaces
title_full_unstemmed The normal distribution in some constrained sample spaces
title_sort The normal distribution in some constrained sample spaces
dc.creator.none.fl_str_mv Mateu Figueras, Gloria
Pawlowsky Glahn, Vera
Egozcue Rubí, Juan José|||0000-0002-5144-4483
author Mateu Figueras, Gloria
author_facet Mateu Figueras, Gloria
Pawlowsky Glahn, Vera
Egozcue Rubí, Juan José|||0000-0002-5144-4483
author_role author
author2 Pawlowsky Glahn, Vera
Egozcue Rubí, Juan José|||0000-0002-5144-4483
author2_role author
author
dc.subject.none.fl_str_mv 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
Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
topic 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
Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
description 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.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01
2014
2014-06-12
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/23204
url https://hdl.handle.net/2117/23204
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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