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

Jupp, P. E.; Regoli, Giuliana; Azzalini, Adelchi

doi:10.1016/j.jmva.2016.02.011

Cited by 12 publications

(12 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…have density function (18). A corollary of the second representation in (19) is the property of perturbation invariance stated next.…”

Section: A General Resultsmentioning

confidence: 91%

“…Even more general formulations, moving along two different paths, are those of Arellano-Valle et al [17] and Jupp et al [18]. However, these treatments encompass also many situations which for technical reasons cannot be pursued operationally.…”

Section: Symmetry-modulated Distributionsmentioning

confidence: 99%

“…The vast majority of the distributions to be discussed later are of type (18) or some 'extended' version of them. The term skew-symmetric distributions is often used to identify these constructions, but we prefer the term symmetry-modulated for the following reason: skewness is typically the form of departure from symmetry associated with linear or mildly non-linear choices of w(x), as it was the case in earlier constructions of this logic, but more elaborate functions w(x) lead to distributions where skewness is not the more prominent feature.…”

Section: Symmetry-modulated Distributionsmentioning

confidence: 99%

“…have density (18). The second form in (22) is more convenient for random number generation, since no rejection of a generated outcome X 0 can occur; the first form allows us to draw connections with a number formulations in applied domains where a selection mechanism of sample values occurs, regulated by a condition of type T ≤ G 0 (X).…”

Section: Symmetry-modulated Distributionsmentioning

confidence: 99%

See 3 more Smart Citations

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Adcock

Azzalini

2020

Symmetry

View full text Add to dashboard Cite

Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.

show abstract

“…have density function (18). A corollary of the second representation in (19) is the property of perturbation invariance stated next.…”

Section: A General Resultsmentioning

confidence: 91%

Section: Symmetry-modulated Distributionsmentioning

confidence: 99%

Section: Symmetry-modulated Distributionsmentioning

confidence: 99%

Section: Symmetry-modulated Distributionsmentioning

confidence: 99%

See 2 more Smart Citations

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Adcock

Azzalini

2020

Symmetry

View full text Add to dashboard Cite

show abstract

“…As far as we know, the only two publications of this sort are those of Azzalini () and Jupp et al. (). The broad target of the present note is to investigate further this area.…”

Section: Background and Aimsmentioning

confidence: 99%

On symmetry‐modulated distributions: revisiting an old result and a step further

Azzalini

Regoli

2018

Stat

View full text Add to dashboard Cite

In the context of modulated-symmetry distributions, there exist various forms of skew-elliptical families. We present yet another one, but with an unusual feature: the modulation factor of the baseline elliptical density is represented by a distribution function with an argument that is not an odd function, as it occurs instead with the overwhelming majority of similar formulations, not only with other skew-elliptical families. The proposal is obtained by going back to the use of a lemma known since 1999, which can be seen as the general frame for a vast number of existing formulations, and use it on a different route. The broader target is to show that this "mother lemma" can still generate novel progeny. The final part of the paper examines a further level of generalization of the "mother-lemma" where symmetry conditions are removed.

show abstract

Generalized Skew-Symmetric Circular and Toroidal Distributions

Bekker

Rad

Arashi

et al. 2022

Forum for Interdisciplinary Mathematics

View full text Add to dashboard Cite

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

Cited by 12 publications

References 18 publications

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

On symmetry‐modulated distributions: revisiting an old result and a step further

Generalized Skew-Symmetric Circular and Toroidal Distributions

Contact Info

Product

Resources

About