The von Mises-Fisher (vMF) distribution has long been a mainstay for inference with data on the unit hypersphere in directional statistics. The performance of statistical inference based on the vMF distribution, however, may suffer when there are significant outliers and noise in the data. Based on an analogy of the median as a robust measure of central tendency and its relationship to the Laplace distribution, we proposed the spherical Laplace (SL) distribution, a novel probability measure for modelling directional data. We present a sampling scheme and theoretical results on maximum likelihood estimation. We derive efficient numerical routines for parameter estimation in the absence of closed-form formula. An application of model-based clustering is considered under the finite mixture model framework. Our numerical methods for parameter estimation and clustering are validated using simulated and real data experiments.

翻译：von Mises-Fisher (vMF) 分布长期以来一直是参照单位超视距数据得出方向统计数据的主要依据。但是,如果数据中存在重大外差和噪音,基于 vMF分布的统计推论工作可能会受到影响。根据中位数的类比,作为衡量中心趋势及其与Laplace分布关系的有力衡量标准,我们提出了球状Laplace (SL) 分布,这是模拟方向数据的新概率衡量标准。我们提出了一个抽样计划和关于最大可能性估算的理论结果。我们在没有封闭式公式的情况下,为参数估算得出有效的数字例行程序。在限定混合物模型框架下考虑采用模型集成。我们参数估计和集集成的数值方法通过模拟和实际数据实验得到验证。