通过布朗运动与包裹柯西分布相关的圆分布族
An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion
摘要：
我们引入了一个与圆上的包裹柯西分布相关的四参数扩展分布族。建议的家庭可以通过改变布朗运动中的问题的设置，产生包装柯西。该族的密度具有封闭形式，并且可以是对称的或不对称的，这取决于参数的选择。三角矩是可用的，他们被证明有一个简单的形式。进一步听话的属性的模型得到，许多利用三角矩。其他主题相关的模型，包括替代衍生和莫比乌斯变换，被认为是。给出了对称子模型的讨论。最后，推广到一个家庭的分布在球面上的简要。
英文摘要：
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 Möbius transformation, are considered. Discussion of the symmetric submodels is given. Finally, generalization to a family of distributions on the sphere is briefly made.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
