• Bernoulli
  • Volume 19, Number 1 (2013), 154-171.

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

Shogo Kato and M.C. Jones

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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 utilizing 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, generalization to a family of distributions on the sphere is briefly made.

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Bernoulli, Volume 19, Number 1 (2013), 154-171.

First available in Project Euclid: 18 January 2013

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asymmetry circular Cauchy distribution directional statistics four-parameter distribution trigonometric moments


Kato, Shogo; Jones, M.C. An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion. Bernoulli 19 (2013), no. 1, 154--171. doi:10.3150/11-BEJ397.

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