Revistes Publicacions URV: SORT - Statistics and Operations Research Transactions> 2013

The normal distribution in some constrained sample spaces

  • Dades identificatives

    Identificador: RP:2393
    Handle: https://hdl.handle.net/20.500.11797/RP2393
    Autors:
    Egozcue, Juan-JoséPawlowsky-Glahn, VeraMateu-Figueras, Glòria
    Resum:
    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.

  • Altres:

    Autor/s de la URV: Egozcue, Juan-José Pawlowsky-Glahn, Vera Mateu-Figueras, Glòria
    Paraules clau: orthonormal basis, simplex additive logistic normal distribution, Aitchison measure, Lebesgue measure lognormal distribution
    Resum: 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.
    Any de publicació de la revista: 2013
    Tipus de publicació: info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article

  • Paraules clau:

    orthonormal basis, simplex
    additive logistic normal distribution, Aitchison measure, Lebesgue measure lognormal distribution

  • Documents:

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