A Mobius transformation-induced distribution on the torus
A Mobius transformation-induced distribution on the torus
复制标题
DOI：
10.1093/biomet/asv003
复制
发表时间：
2015-06-01
期刊：
影响因子：
2.7
通讯作者：
Pewsey, Arthur
中科院分区：
文献类型：
--
作者：
Kato, Shogo;Pewsey, Arthur
我们提出了一个五参数双变量包裹柯西分布作为单峰模型的环形数据。它是高度易处理的，显示了许多理想的属性，包括边缘和条件分布，都包裹柯西，并出现作为一个有吸引力的子模型的六参数分布通过应用莫比乌斯变换到一个预先存在的二元循环模型。矩量法及其参数的最大似然估计速度很快，并且可以进行独立性和拟合优度测试。蛋白质氨基酸酪氨酸二面角的分析说明了分布的应用。还探讨了循环数据的马尔可夫过程。
We propose a five-parameter bivariate wrapped Cauchy distribution as a unimodal model for toroidal data. It is highly tractable, displays numerous desirable properties, including marginal and conditional distributions that are all wrapped Cauchy, and arises as an appealing submodel of a six-parameter distribution obtained by applying Mobius transformation to a pre-existing bivariate circular model. Method of moments and maximum likelihood estimation of its parameters are fast, and tests for independence and goodness-of-fit are available. An analysis involving dihedral angles of the proteinogenic amino acid Tyrosine illustrates the distribution's application. A Markov process for circular data is also explored.