The need for statistical models of orientations arises in many applications in engineering and computer science. Orientational data appear as sets of angles, unit vectors, rotation matrices or quaternions. In the field of directional statistics, a lot of advances have been made in modelling such types of data. However, only a few of these tools are used in engineering and computer science applications. Hence, this paper aims to serve as a cheat sheet for those probability distributions of orientations. Models for 1-DOF, 2-DOF and 3-DOF orientations are discussed. For each of them, expressions for the density function, fitting to data, and sampling are presented. The paper is written with a compromise between engineering and statistics in terms of notation and terminology. A Python library with functions for some of these models is provided. Using this library, two examples of applications to real data are presented.

翻译：在工程与计算机科学的诸多应用中，常需建立方向数据的统计模型。方向数据可表现为角度集、单位向量、旋转矩阵或四元数等形式。在方向统计学领域，此类数据的建模方法已取得显著进展。然而，工程与计算机科学领域实际应用中仅采纳了其中少数工具。为此，本文旨在为方向概率分布提供一份速查指南。文中讨论了单自由度、双自由度及三自由度方向模型，针对每种模型分别给出概率密度函数表达式、数据拟合方法及采样技术。本文在符号与术语使用上兼顾了工程学与统计学的表达习惯。同时提供了包含部分模型函数的Python库，并运用该库展示了两个实际数据应用的示例。