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Inverse Batschelet distributions for circular data

Jones, M. C. and Pewsey, Arthur (2012). Inverse Batschelet distributions for circular data. Biometrics, 68(1) pp. 183–193.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1111/j.1541-0420.2011.01651.x
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Abstract

We provide four-parameter families of distributions on the circle which are unimodal and display the widest ranges of both skewness and peakedness yet available. Our approach is to transform the scale of a generating distribution, such as the von Mises, using various nontrivial extensions of an approach first used in Batschelet’s (1981, Circular Statistics in Biology) book. The key is to employ inverses of Batschelet-type transformations in certain ways; these exhibit considerable advantages over direct Batschelet transformations. The skewness transformation is especially appealing as it has no effect on the normalizing constant. As well as a variety of interesting theoretical properties, when likelihood inference is explored these distributions display orthogonality between elements of a pairing of parameters into (location, skewness) and (concentration, peakedness). Further, the location parameter can sometimes be made approximately orthogonal to all the other parameters. Profile likelihoods come to the fore in practice. Two illustrative applications, one concerning the locomotion of a Drosophila fly larva, the other analyzing a large set of sudden infant death syndrome data, are investigated.

Item Type: Journal Article
Copyright Holders: 2011 The International Biometric Society
ISSN: 1541-0420
Keywords: circular statistics; flat-topped; parameter orthogonality; skew distributions; transformation of scale; unimodality; von Mises distribution
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30448
Depositing User: M. C. Jones
Date Deposited: 12 Dec 2011 10:41
Last Modified: 30 Nov 2012 10:44
URI: http://oro.open.ac.uk/id/eprint/30448
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