A cheat sheet for probability distributions of orientational data

Lopez-Custodio, PC ORCID: https://orcid.org/0000-0002-3914-6029, 2025. A cheat sheet for probability distributions of orientational data. Mechanism and Machine Theory. ISSN 0094-114X (Forthcoming)

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Abstract

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.

Item Type:	Journal article
Publication Title:	Mechanism and Machine Theory
Creators:	Lopez-Custodio, P.C.
Publisher:	Elsevier
Date:	11 March 2025
ISSN:	0094-114X
Identifiers:	Number Type 2403493 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Jonathan Gallacher
Date Added:	13 Mar 2025 11:23
Last Modified:	13 Mar 2025 11:23
URI:	https://irep.ntu.ac.uk/id/eprint/53238

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