A possibly asymmetric multivariate generalization of the Möbius distribution for directional data
A possibly asymmetric multivariate generalization of the Möbius distribution for directional data
复制标题
方向数据莫比乌斯分布的可能不对称多元推广
DOI：
10.1016/j.jmva.2014.11.004
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. SenGupta
中科院分区：
文献类型：
--
作者：
K. Uesu;K. Shimizu;A. SenGupta
提出了一类中心在原点的单位超圆盘上的可能非对称分布族。本文给出了单位圆盘上Möbius分布的一个非平凡的多元推广。该族是通过将保角映射应用于球对称β分布而获得的。族的密度函数是单峰的、单调的或单反峰的。给定长度的方向余弦的条件分布是球面上的t分布。给定方向余弦的长度的条件分布有一个简单的封闭形式表达式，尽管不是任何标准的已知分布。模态、偏度和方向参数在Fisher信息矩阵是对角的意义上是全局正交的。建议的模型上的超光盘，引入这种概率分布的第一次，适用于天体物理学的一个新兴领域的数据集的伽玛射线暴和地球信息学的一个具有挑战性的领域的数据集的全球地震震级大于或等于7.0兆瓦。
A family of possibly asymmetric distributions on the unit hyper-disc with center at the origin is proposed. The paper presents a non-trivial multivariate generalization of the Möbius distribution on the unit disc. The family is obtained by applying a conformal mapping to the spherically symmetric beta distribution. The density functions of the family are unimodal, monotonic or uniantimodal. The conditional distribution of direction cosine given the length is a t-distribution on the sphere. The conditional distribution of the length given the direction cosine has a simple closed form expression, though not of any standard known distribution. Modality, skewness and direction parameters are globally orthogonal in the sense that the Fisher information matrix is diagonal. The proposed model on the hyper-disc, introducing this probability distribution for the very first time, is applied to an emerging area of astrophysics for a dataset on gamma-ray bursts and to a challenging area of geoinformatics for a dataset on worldwide earthquakes with magnitude greater than or equal to 7.0 M W.