We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by parameters with meaningful statistical interpretations that can range over the entire real space of an adequate dimension. The new parameterization greatly simplifies maximum likelihood estimation of all model parameters, which in turn leads to theoretically sound and numerically stable inference procedures to infer key features of the distribution. Byproducts from the likelihood-based inference are used to develop graphical and numerical diagnostic tools for assessing goodness of fit of this distribution in a data application. Simulation study and application to data from a hydrogeology study are used to demonstrate implementation and performance of the inference procedures and diagnostics methods.

翻译：我们设计了一组角高斯分布法, 允许任意尺寸方向随机变量有不同程度的异向随机变量。 通过一系列新的重新校准度, 这个分布式组通过具有有意义的统计解释的参数进行索引化, 这些参数可以覆盖一个适当尺寸的整个实际空间。 新的参数化极大地简化了所有模型参数的最大可能性估计, 这反过来导致在理论上合理和数字上稳定的推导程序, 以推断分布的关键特征。 从概率推论得出的副产品被用来开发图形和数字诊断工具, 用以评估数据应用中这种分布的适宜性。 模拟研究和对水文地质学研究数据的应用被用来演示推断程序和诊断方法的实施和性能 。