A cylindrical distribution with heavy-tailed linear part
A cylindrical distribution with heavy-tailed linear part
复制标题
具有重尾线性部分的圆柱分布
DOI：
10.1007/s42081-019-00031-5
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发表时间：
2019
影响因子：
1.3
通讯作者：
Toshihiro Abe
中科院分区：
文献类型：
--
作者：
Tomoaki Imoto;Kunio Shimizu;Toshihiro Abe
提出了一种线性部分模拟重尾性的圆柱分布。给定循环变量的线性变量的条件分布是广义帕累托型分布。因此，它可能没有任何条件矩;但是，众数和中位数具有封闭形式的表达式。圆形边缘分布是一个包裹柯西分布，而给定线性变量的圆形变量的条件分布属于对称分布族。这些属性允许其应用到圆柱形数据，其线性观测值可能会取较大的值，其圆形观测值是对称的。作为说明性的例子，建议的分布拟合到两个数据集，并与其他圆柱形分布，不能模型的线性部分重尾的结果进行比较。
A cylindrical distribution whose linear part models heavy-tailedness is proposed. The conditional distribution of the linear variable given the circular variable is a generalized Pareto-type distribution. Therefore, it may not have any conditional moments; however, the mode and median have closed-form expressions. The circular marginal distribution is a wrapped Cauchy distribution, and the conditional distribution of the circular variable given the linear variable belongs to a family of symmetric distributions. These properties allow its application to cylindrical data, whose linear observations may take large values and whose circular observations are symmetric. As illustrative examples, the proposed distribution is fitted to two data sets, and the results are compared with those by other cylindrical distributions that cannot model heavy-tailedness for the linear parts.