Emergence of the wrapped Cauchy distribution in mixed directional data

Joseph D. Bailey () and Edward A. Codling
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Joseph D. Bailey: University of Essex
Edward A. Codling: University of Essex

AStA Advances in Statistical Analysis, 2021, vol. 105, issue 2, No 2, 229-246

Abstract: Abstract 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.

Keywords: Circular distributions; Wrapped normal; Wrapped Cauchy; Animal movement; Directional data; MSC 62P10; MSC 92B05 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10182-020-00380-7

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