定向数据的概率分布的备忘表

IF 4.5 1区工程技术 Q1 ENGINEERING, MECHANICAL

Mechanism and Machine Theory Pub Date : 2025-04-08 DOI:10.1016/j.mechmachtheory.2025.105995

P.C. López-Custodio

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引用次数: 0

摘要

在工程和计算机科学的许多应用中都出现了对方位统计模型的需求。方向数据表现为角度、单位矢量、旋转矩阵或四元数的集合。在方向统计领域，这类数据的建模已经取得了很大的进展。然而，这些工具中只有少数用于工程和计算机科学应用。因此，本文旨在为这些方向的概率分布提供备忘单。讨论了1-DOF、2-DOF和3-DOF方向的模型。对于每一种方法，给出了密度函数、数据拟合和抽样的表达式。这篇论文在符号和术语方面是工程学和统计学之间的妥协。提供了一个Python库，其中包含一些模型的函数。利用该库，给出了两个应用于实际数据的实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A cheat sheet for probability distributions of orientational data

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.

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来源期刊

Mechanism and Machine Theory 工程技术-工程：机械

CiteScore

9.90

自引率

23.10%

发文量

450

审稿时长

20 days

期刊介绍： Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal. The main topics are: Design Theory and Methodology; Haptics and Human-Machine-Interfaces; Robotics, Mechatronics and Micro-Machines; Mechanisms, Mechanical Transmissions and Machines; Kinematics, Dynamics, and Control of Mechanical Systems; Applications to Bioengineering and Molecular Chemistry