论文标题
方向分布和半角度原理
Directional distributions and the half-angle principle
论文作者
论文摘要
在研究方向分布时，角度减半或角度加倍的反向操作是一个有用的工具。它在圆上特别有用，特别是在圆圈中，它在包裹的考奇分布和角中央高斯分布以及其参数化的匹配之间产生识别。角度减半的操作可以扩展到更高的尺寸，但其对分布的影响比在圆圈上更为复杂。在各个维度上，角度减半提供了一种简单的方法来解释从球体到欧几里得空间的立体投影。
Angle halving, or alternatively the reverse operation of angle doubling, is a useful tool when studying directional distributions. It is especially useful on the circle where, in particular, it yields an identification between the wrapped Cauchy distribution and the angular central Gaussian distributions, as well as a matching of their parameterizations. The operation of angle halving can be extended to higher dimensions, but its effect on distributions is more complicated than on the circle. In all dimensions angle halving provides a simple way to interpret stereographic projection from the sphere to Euclidean space.
