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首页> 外文期刊>Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability >An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion
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An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion

机译：扩展的圆形分布族与通过布朗运动包裹的柯西分布有关

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摘要

We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped Cauchy. The densities of this family have a closed form and can be symmetric or asymmetric depending on the choice of the parameters. Trigonometric moments are available, and they are shown to have a simple form. Further tractable properties of the model are obtained, many by utilizing the trigonometric moments. Other topics related to the model, including alternative derivations and M?bius transformation, are considered. Discussion of the symmetric submodels is given. Finally, generalization to a family of distributions on the sphere is briefly made.
机译：我们介绍了一个与圆上包裹的柯西分布有关的四参数扩展族。可以通过更改布朗运动中产生包裹柯西的问题的设置来派生所提出的族。该族的密度具有闭合形式，并且可以取决于参数的选择而对称或不对称。三角矩是可用的，并且显示为具有简单的形式。通过利用三角矩，可以获取模型的其他易处理特性。考虑与模型相关的其他主题，包括替代推导和M？bius变换。讨论了对称子模型。最后，简要介绍了球面上的分布族。

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