The Möbius distribution on the disc
The Möbius distribution on the disc
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圆盘上的莫比乌斯分布
DOI：
10.1007/bf02506486
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发表时间：
2004
影响因子：
1
通讯作者：
M. C. Jones
中科院分区：
文献类型：
--
作者：
M. C. Jones
提出了一种新的简单分布族，它在二维空间上支持单位圆盘。族的密度函数为单峰、单调或单反峰。二元对称分布，包括均匀分布，是特殊情况，但家族的许多成员是倾斜的。分布有三个参数，一个控制方向，一个控制浓度，第三个控制偏度，或者更准确地说，偏离中心。重要的是，这些参数是全局正交的。给出了模型与数据拟合的实例。考虑了条件分布和边际分布。新的发行版与同一作者早先提出的建议进行了比较。
A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.