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The wrapped t family of circular distributions

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

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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 Item
Copyright Holders: 2007 Australian Statistical Publishing Association Inc.
ISSN: 1467-842X
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/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 15658
Depositing User: Colin Smith
Date Deposited: 16 Apr 2009 11:41
Last Modified: 07 Dec 2018 09:21
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