On a class of circulas: copulas for circular distributions

Jones, M. C.; Pewsey, Arthur; Kato, Shogo

doi:10.1007/s10463-014-0493-6

Cited by 34 publications

(34 citation statements)

References 34 publications

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“…For X = S 1 , Jones et al [12] point out that it is convenient to take θ 0 to be the mode (assumed unique) of µ. If the dimension of X is greater than 1 then the homeomorphism φ is not unique, even if φ is required to keep some given point fixed.…”

Section: Uniform Distributionsmentioning

confidence: 99%

“…For G = S 1 , this construction is that considered by Wehrly & Johnson [28] and Jones et al [12]. Special cases of the corresponding stationary Markov processes were given in models 3.1 and 3.4 of [1].…”

Section: Mixed Translation Copulae On Compact Lie Groupsmentioning

confidence: 99%

“…Copulae on the circle, called 'circulae', have been developed by Jones, Pewsey & Kato [12], who pay particular attention to a method of constructing circulae using convolution, special cases of which had appeared in [10], [8], [11] and [28]. The aim of this paper is to extend the idea of circula to a concept of copula on compact Riemannian manifolds, which are the main sample spaces considered in directional statistics.…”

Section: Introductionmentioning

confidence: 99%

“…Section 4 considers two general constructions of copulae on compact Lie groups and their coset spaces. One of these extends the convolution construction in [12] of circulae; the other is based on the Sobolev mappings used in directional statistics. Examples involving paired data on the sphere and on the rotation group, SO(3), are given in Section 5.…”

Section: Introductionmentioning

confidence: 99%

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Copulae on products of compact Riemannian manifolds

Jupp

2015

Journal of Multivariate Analysis

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Please cite this article as: P.E. Jupp, Copulae on products of compact Riemannian manifolds, Journal of Multivariate Analysis (2015), http://dx.doi.org/10.1016/j.jmva. 2015.04.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Copulae on products of compact Riemannian manifolds P. E. JuppSchool of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK AbstractOne standard way of considering a probability distribution on the unit ncube, [0, 1] n

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Section: Uniform Distributionsmentioning

confidence: 99%

Section: Mixed Translation Copulae On Compact Lie Groupsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Copulae on products of compact Riemannian manifolds

Jupp

2015

Journal of Multivariate Analysis

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“…For instance Jones et al (2015) introduced copulas for circular distributions while Kato and Jones (2010 introduced families of distributions on the circle obtained via different techniques. Density estimation on the circle was considered in García-Portugués et al (2013) while Oliveira et al (2014aOliveira et al ( , 2014b provided practical tools to deal with circular data.…”

Section: Introductionmentioning

confidence: 99%

Le Cam maximin tests for symmetry of circular data based on the characteristic function

Meintanis¹,

Verdebout²

2019

STAT SINICA

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We consider asymptotic inference for circular data based on the empirical characteristic function. More precisely, we provide tests for reflective symmetry of circular data based on the imaginary part of the empirical characteristic function.We show that the proposed tests enjoy many attractive features. In particular, we obtain that they enjoy the property of being locally and asymptotically maximin in the Le Cam sense under sine-skewed alternatives in the specified mean direction case. To the best of our knowledge, this result provides the first instance of such an optimality property of empirical characteristic functions. For the unspecified mean direction case, we provide corrected versions of the original tests that keep very nice asymptotic power properties. Results are illustrated on a well-known dataset and checked via Monte-Carlo simulations.

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Directional Distributions

Mardia¹,

Ley²

2018

Wiley StatsRef: Statistics Reference Online

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Various practical situations give rise to observations that are directions, and this has led to the field of directional statistics. Especially in recent years, new applications of this area have emerged, such as in structural bioinformatics, machine learning and cosmology. Consequently, various new directional distributions have appeared in the literature including on the circle, sphere, cylinder, torus, among others. These distributions take into account the underlying manifold. In this article, we provide a thorough review of the most important directional distributions with their main properties. Wherever relevant, we also give some indication of the particular application area which has led to a specific distribution.

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On a class of circulas: copulas for circular distributions

Cited by 34 publications

References 34 publications

Copulae on products of compact Riemannian manifolds

Copulae on products of compact Riemannian manifolds

Le Cam maximin tests for symmetry of circular data based on the characteristic function

Directional Distributions

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