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28 p, 389.4 KB The normal distribution in some constrained sample spaces / Mateu-Figueras, Glòria (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ; Pawlowsky-Glahn, Vera (Universitat de Girona. Departament d'Informàtica i Matemàtica Aplicada) ; Egozcue, Juan-José (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
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. [...]
SORT : statistics and operations research transactions, Vol. 37, Núm. 1 (January-June 2013) , p. 29-56  

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