文章基本信息

标题：The normal distribution in some constrained sample spaces
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作者：Glòria Mateu-Figueras ; Vera Pawlowsky-Glahn ; Juan-José Egozcue 等
期刊名称：SORT-Statistics and Operations Research Transactions
印刷版ISSN：2013-8830
出版年度：2013
卷号：37
期号：1
页码：29-56
语种：English
出版社：SORT- Statistics and Operations Research Transactions
摘要：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.
关键词：additive logistic normal distribution, Aitchison measure, Lebesgue measure lognormal distribution;orthonormal basis, simplex