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Emergence of the wrapped Cauchy distribution in mixed directional data

Bailey, Joseph D and Codling, Edward A (2021) 'Emergence of the wrapped Cauchy distribution in mixed directional data.' AStA Advances in Statistical Analysis, 105 (2). pp. 229-246. ISSN 0002-6018

ASTB-D-19-00251_R1.pdf - Accepted Version

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Inferring the most appropriate distribution (or distributions) to describe observed directional data is important in many applications of circular statistics. In particular, animal movement paths are typically analysed and modelled by considering the distribution of step lengths and turning (or absolute) angles. Here we demonstrate that a single-wrapped Cauchy distribution can appear to fit directional data mixed from two different underlying wrapped normal distributions. We derive mathematical expressions to calculate the parameter space for which this occurs and illustrate the result by analysing an example data set of the movements of African bull elephants (Loxodonta Africana). We conclude that the presence of a wrapped Cauchy distribution in observed directional data can, in certain cases, be explained by data coming from two distinct underlying distributions. We discuss how this may relate to the presence of multiple movement modes within an observed path when analysing animal movement data.

Item Type: Article
Uncontrolled Keywords: Circular distributions; Wrapped normal; Wrapped Cauchy; Animal movement; Directional data
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 09 Oct 2020 10:49
Last Modified: 18 Aug 2022 12:32

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