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An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion

Kato, Shogo and Jones, M. C. (2013). An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion. Bernoulli, 19(1) pp. 154–171.

URL: http://www.e-publications.org/ims/submission/index...
DOI (Digital Object Identifier) Link: http://dx.doi.org/10.3150/11-BEJ397
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Abstract

We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped Cauchy. The densities of this family have a closed form and can be symmetric or asymmetric depending on the choice of the parameters. Trigonometric moments are available, and they are shown to have a simple form. Further tractable properties of the model are obtained, many by utilising the trigonometric moments. Other topics related to the model, including alternative derivations and Möbius transformation are considered. Discussion of the symmetric submodels is given. Finally, generalisation to a family of distributions on the sphere is briefly made.

Item Type: Journal Article
Copyright Holders: 2013 ISI/BS
ISSN: 1350-7265
Keywords: asymmetry; circular Cauchy distribution; directional statistics; four-parameter distribution; trigonometric moments
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30449
Depositing User: M. C. Jones
Date Deposited: 12 Dec 2011 10:59
Last Modified: 30 Jan 2013 15:24
URI: http://oro.open.ac.uk/id/eprint/30449
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