Two new distributions are proposed: the circular projected and the spherical projected Cauchy distributions. A special case of the circular projected Cauchy coincides with the wrapped Cauchy distribution, and for this, a generalization is suggested that offers better fit via the inclusion of an extra parameter. For the spherical case, by imposing two conditions on the scatter matrix we end up with an elliptically symmetric distribution. All distributions allow for a closed-form normalizing constant and straightforward random values generation, while their parameters can be estimated via maximum likelihood. The bias of the estimated parameters is assessed via numerical studies, while exhibitions using real data compare them further to some existing models indicating better fits.

翻译：提出两种新分布：圆形投影柯西分布和球形投影柯西分布。圆形投影柯西分布的一个特例与包裹柯西分布一致，为此我们通过引入额外参数提出一种泛化形式，从而获得更好的拟合效果。对于球形情形，通过对方差-协方差矩阵施加两个约束条件，最终得到椭圆对称分布。所有分布均具有闭合形式的归一化常数和直接的随机数生成方法，其参数可通过最大似然估计进行估计。通过数值研究评估估计参数的偏差，并利用真实数据与现有模型进行比较，结果表明新分布具有更好的拟合效果。