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On a class of circulas: copulas for circular distributions

Jones, M. C.; Pewsey, Arthur and Kato, Shogo (2015). On a class of circulas: copulas for circular distributions. Annals of the Institute of Statistical Mathematics, 67(5) pp. 843–862.

DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s10463-014-0493-6
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Abstract

This article is concerned with the analogue of copulas for circular distributions, which we call ‘circulas’. We concentrate on one particular class of circulas, which is pre-existing but not studied in such explicit form or detail before. This class is appealing in many ways but does not necessarily result in especially attractive bivariate circular models for arbitrary non-uniform marginals. A major exception to this is an elegant bivariate wrapped Cauchy distribution previously proposed and developed by two of the current authors. We look both at properties of the circulas themselves, including their density behaviour, distribution function, and dependence measures, and at properties of various distributions based on these circulas by transformation to non-uniform marginal distributions. We consider inference for the latter distributions and present two applications of them to modelling data. We concentrate mostly on the bivariate case, but also briefly consider extension to the multivariate case.

Item Type: Journal Item
Copyright Holders: 2014 The Institute of Statistical Mathematics
ISSN: 1572-9052
Project Funding Details:
Funded Project NameProject IDFunding Body
GrantMTM2010-16845e Spanish Ministry of Science and Education
GrantGR10064Junta de Extremadura
Keywords: Bivariate; circular distributions; copula; dependence; multivariate; torus
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 44632
Depositing User: M. C. Jones
Date Deposited: 16 Oct 2015 14:40
Last Modified: 24 May 2019 09:30
URI: http://oro.open.ac.uk/id/eprint/44632
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