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The wrapped t family of circular distributions

Pewsey, A.; Lewis, T. and Jones, M.C. (2007). The wrapped t family of circular distributions. Australian and New Zealand Journal of Statistics, 49(1) pp. 79–91.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1111/j.1467-842X.2006.00465.x
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Abstract

This paper considers the three-parameter family of symmetric unimodal distributions obtained by wrapping the location-scale extension of Student's t distribution onto the unit circle. The family contains the wrapped normal and wrapped Cauchy distributions as special cases, and can be used to closely approximate the von Mises distribution. In general, the density of the family can only be represented in terms of an infinite summation, but its trigonometric moments are relatively simple expressions involving modified Bessel functions. Point estimation of the parameters is considered, and likelihood-based methods are used to fit the family of distributions in an illustrative analysis of cross-bed measurements. The use of the family as a means of approximating the von Mises distribution is investigated in detail, and new efficient algorithms are proposed for the generation of approximate pseudo-random von Mises variates.

Item Type: Journal Article
ISSN: 1369-1473
Keywords: Bessel functions; Symmetry; Cauchy problem; Algorithms; Transcendental functions; Efficient von Mises simulation; Modified Bessel function; Unimodality; von Mises distribution; Wrapped Cauchy distribution; Wrapped normal distribution;
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 15658
Depositing User: Colin Smith
Date Deposited: 16 Apr 2009 11:41
Last Modified: 02 Dec 2010 20:26
URI: http://oro.open.ac.uk/id/eprint/15658
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