摘要翻译：
样本空间受限的现象在实践中经常出现。例如，对于严格的正数据和组成数据，例如百分比等等，情况就是这样。如果差分的自然测度不是绝对测度，就有可能用简单的代数性质来表明，用一个不是真实空间中通常的欧几里得几何的几何和一个不是通常的勒贝格测度的测度来工作更方便，从而导致更适合所研究的现象的替代模型。给出了正实线和D部分单纯形上的一般方法，并加以说明。
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英文标题：
《The normal distribution in some constrained sample spaces》
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作者：
G. Mateu-Figueras, V. Pawlowsky-Glahn, J.J. Egozcue
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最新提交年份：
2008
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute one, it is possible to use simple algebraic properties to show that it is more convenient to work with a geometry that is not the usual Euclidean geometry in real space, and with a measure which is not the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated both on the positive real line and on the D-part simplex.
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PDF链接：
https://arxiv.org/pdf/802.2643