A distribution for a pair of unit vectors generated by Brownian motion
A distribution for a pair of unit vectors generated by Brownian motion
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DOI：
10.3150/08-bej178
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发表时间：
2009-08
期刊：
影响因子：
1.5
通讯作者：
Shogo Kato
中科院分区：
文献类型：
--
作者：
Shogo Kato
提出了一个由布朗运动生成的相依单位向量对的二元模型。这两个边缘函数在球面上都有均匀分布，而条件函数遵循所谓的“退出”分布。研究了该模型的参数估计和一个关键统计量的性质。通过将变量和参数转换为复数形式，对二元循环情形进行了进一步的研究。一些理想的性质，如乘法性质和无限可分性，保持这个子模型。研究了子模型参数的两种估计，并进行了模拟研究，以探讨估计的有限样本性能。在尝试产生更灵活的模型，一些方法来推广所提出的模型进行了讨论。其中一个广义模型适用于风向数据。最后，我们展示了如何通过将双线性分数变换应用于所提出的双变量圆形模型来构造平面和圆柱上的分布。
We propose a bivariate model for a pair of dependent unit vectors which is generated by Brownian motion. Both marginals have uniform distributions on the sphere, while the conditionals follow so-called "exit" distributions. Some properties of the proposed model, including parameter estimation and a pivotal statistic, are investigated. Further study is undertaken for the bivariate circular case by transforming variables and parameters into the form of complex numbers. Some desirable properties, such as a multiplicative property and infinite divisibility, hold for this submodel. Two estimators for the parameter of the submodel are studied and a simulation study is carried out to investigate the finite sample performance of the estimators. In an attempt to produce more flexible models, some methods to generalize the proposed model are discussed. One of the generalized models is applied to wind direction data. Finally, we show how it is possible to construct distributions in the plane and on the cylinder by applying bilinear fractional transformations to the proposed bivariate circular model.