文章基本信息

标题：Stochastic representations and a geometric parametrization of the two-dimensional Gaussian law
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作者：Thomas Dietrich ; Steve Kalke ; Wolf-Dieter Richter 等
期刊名称：Chilean Journal of Statistics
印刷版ISSN：0718-7912
电子版ISSN：0718-7920
出版年度：2013
卷号：4
期号：2
页码：27-59
出版社：Chilean Statistical Society
摘要：Using di.erent types of polar and elliptical p olar coordinates, di.erent stochastic rep- resentations of the axis-aligned and the regular two-dimensional Gaussian distribution are derived. Advantages and disadvantages of these stochastic representations are dis- cussed. The non-Euclidean geometric measure representation of the axis-aligned two- dimensional Gaussian distribution in Richter (2011) is taken to derive a new geo- metric interpretation of the correlation co e.cient and to motivate a new geometric parametrization of the regular Gaussian law. Estimators of the new parameters and corresponding distributions are derived. A comparison with di.erent approaches from the literature shows the numerical stability of our results.
关键词：Sto chastic representations ; random coordinates ; maximum likeliho od ; estimation ; exact distributions ; correlation