A Family of symmetric distributions on the circle

Jones, M.C. and Pewsey, Arthur (2005). A Family of symmetric distributions on the circle. Journal of the American Statistical Association, 100(472) pp. 1422–1428.

DOI: https://doi.org/10.1198/016214505000000286

Abstract

We propose a new family of symmetric unimodal distributions on the circle that contains the uniform, von Mises, cardioid, and wrapped Cauchy distributions, among others, as special cases. The basic form of the densities of this family is very simple, although its normalization constant involves an associated Legendre function. The family of distributions can also be derived by conditioning and projecting certain bivariate spherically and elliptically symmetric distributions on to the circle. Trigonometric moments are available, and a measure of variation is discussed. Aspects of maximum likelihood estimation are considered, and likelihood is used to fit the family of distributions to an example set of data. Finally, extension to a family of rotationally symmetric distributions on the sphere is briefly made.

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About

• Item ORO ID
• 2136
• Item Type
• Journal Item
• ISSN
• 1537-274X
• Keywords
• associated Legendre function; cardioid distribution; circular uniform distribution; distributions on the sphere; Von Mises distribution; wrapped Cauchy distribution;
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• M. C. Jones