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dc.contributor.authorJupp, P.E.
dc.identifier.citationJupp , P E 2015 , ' Copulae on products of compact Riemannian manifolds ' , Journal of Multivariate Analysis , vol. 140 , pp. 92-98 .
dc.identifier.otherPURE: 186712169
dc.identifier.otherPURE UUID: f633416f-a409-47ec-867d-fc79dffdd159
dc.identifier.otherBibtex: urn:25ca5439b7dd9c27e03ce09bd1b4076d
dc.identifier.otherScopus: 84929346942
dc.identifier.otherORCID: /0000-0003-0973-8434/work/60195542
dc.identifier.otherWOS: 000359033100007
dc.description.abstractAbstract One standard way of considering a probability distribution on the unit n -cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [0 , 1]n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data.
dc.relation.ispartofJournal of Multivariate Analysisen
dc.rightsCopyright © 2015 Published by Elsevier Inc. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectUniform scoresen
dc.subjectHomogeneous manifolden
dc.subjectMarkov processen
dc.subjectUniform distributionen
dc.subjectQA Mathematicsen
dc.titleCopulae on products of compact Riemannian manifoldsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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