Skip to content

Research at St Andrews

A general setting for symmetric distributions and their relationship to general distributions

Research output: Contribution to journalArticlepeer-review

Standard

A general setting for symmetric distributions and their relationship to general distributions. / Jupp, P.E.; Regoli, G.; Azzalini, A.

In: Journal of Multivariate Analysis, Vol. 148, 06.2016, p. 107-119.

Research output: Contribution to journalArticlepeer-review

Harvard

Jupp, PE, Regoli, G & Azzalini, A 2016, 'A general setting for symmetric distributions and their relationship to general distributions', Journal of Multivariate Analysis, vol. 148, pp. 107-119. https://doi.org/10.1016/j.jmva.2016.02.011

APA

Jupp, P. E., Regoli, G., & Azzalini, A. (2016). A general setting for symmetric distributions and their relationship to general distributions. Journal of Multivariate Analysis, 148, 107-119. https://doi.org/10.1016/j.jmva.2016.02.011

Vancouver

Jupp PE, Regoli G, Azzalini A. A general setting for symmetric distributions and their relationship to general distributions. Journal of Multivariate Analysis. 2016 Jun;148:107-119. https://doi.org/10.1016/j.jmva.2016.02.011

Author

Jupp, P.E. ; Regoli, G. ; Azzalini, A. / A general setting for symmetric distributions and their relationship to general distributions. In: Journal of Multivariate Analysis. 2016 ; Vol. 148. pp. 107-119.

Bibtex - Download

@article{57f039889fa24755816f87a19a2c2558,
title = "A general setting for symmetric distributions and their relationship to general distributions",
abstract = "A standard method of obtaining non-symmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.",
keywords = "Directional statistics, Skew-symmetric distribution, Symmetry-modulated distribution, Transformation",
author = "P.E. Jupp and G. Regoli and A. Azzalini",
year = "2016",
month = jun,
doi = "10.1016/j.jmva.2016.02.011",
language = "English",
volume = "148",
pages = "107--119",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - A general setting for symmetric distributions and their relationship to general distributions

AU - Jupp, P.E.

AU - Regoli, G.

AU - Azzalini, A.

PY - 2016/6

Y1 - 2016/6

N2 - A standard method of obtaining non-symmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.

AB - A standard method of obtaining non-symmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.

KW - Directional statistics

KW - Skew-symmetric distribution

KW - Symmetry-modulated distribution

KW - Transformation

U2 - 10.1016/j.jmva.2016.02.011

DO - 10.1016/j.jmva.2016.02.011

M3 - Article

VL - 148

SP - 107

EP - 119

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -

Related by author

  1. Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds

    Jupp, P. E. & Kume, A., Mar 2020, In: Journal of Multivariate Analysis. 176, 104579.

    Research output: Contribution to journalArticlepeer-review

  2. Orientations of symmetrical objects

    Jupp, P. E. & Arnold, R., 2019, Applied Directional Statistics: Modern Methods and Case Studies. Ley, C. & Verdebout, T. (eds.). Boca Raton, London, New York: CRC Press, p. 25-44 20 p.

    Research output: Chapter in Book/Report/Conference proceedingChapter

  3. Bimodal or quadrimodal? Statistical tests for the shape of fault patterns

    Healy, D. & Jupp, P., 22 Aug 2018, In: Solid Earth. 9, 4, p. 1051-1060 10 p.

    Research output: Contribution to journalArticlepeer-review

  4. Statistics of ambiguous rotations

    Arnold, R., Jupp, P. E. & Schaeben, H., May 2018, In: Journal of Multivariate Analysis. 165, p. 73-85

    Research output: Contribution to journalArticlepeer-review

  5. Copulae on products of compact Riemannian manifolds

    Jupp, P. E., Sep 2015, In: Journal of Multivariate Analysis. 140, p. 92-98

    Research output: Contribution to journalArticlepeer-review

Related by journal

  1. Measures of goodness of fit obtained by almost-canonical transformations on Riemannian manifolds

    Jupp, P. E. & Kume, A., Mar 2020, In: Journal of Multivariate Analysis. 176, 104579.

    Research output: Contribution to journalArticlepeer-review

  2. Statistics of ambiguous rotations

    Arnold, R., Jupp, P. E. & Schaeben, H., May 2018, In: Journal of Multivariate Analysis. 165, p. 73-85

    Research output: Contribution to journalArticlepeer-review

  3. Copulae on products of compact Riemannian manifolds

    Jupp, P. E., Sep 2015, In: Journal of Multivariate Analysis. 140, p. 92-98

    Research output: Contribution to journalArticlepeer-review

  4. New discrete Appell and Humbert distributions with relevance to bivariate accident data

    Kemp, A. W., Jan 2013, In: Journal of Multivariate Analysis. 113, p. 2-6 5 p.

    Research output: Contribution to journalArticlepeer-review

ID: 241247270

Top