On bivariate transformation of scale distributions

Elsewhere, I have promoted (univariate continuous) "transformation of scale" (ToS) distributions having densities of the form 2g(Π −1 (x)) where g is a symmetric distribution and Π is a transformation function with a special property. Here, I develop bivariate (readily multivariate) ToS di...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2016-02, Vol.45 (3), p.577-588
Main Author: Jones, M.C.
Format: Article
Language:English
Subjects:
Bivariate inverse Gaussian distribution
Covariance
Density
Inverse
Joints
Normal distribution
R-symmetry
Sinh-arcsinh transformation
Skew-symmetric distribution
Statistics
Symmetry
Transformations
Transformations (mathematics)
Two-piece distribution
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Summary:Elsewhere, I have promoted (univariate continuous) "transformation of scale" (ToS) distributions having densities of the form 2g(Π −1 (x)) where g is a symmetric distribution and Π is a transformation function with a special property. Here, I develop bivariate (readily multivariate) ToS distributions. Univariate ToS distributions have a transformation of random variable relationship with Azzalini-type skew-symmetric distributions; the bivariate ToS distribution here arises from marginal variable transformation of a particular form of bivariate skew-symmetric distribution. Examples are given, as are basic properties-unimodality, a covariance property, random variate generation-and connections with a bivariate inverse Gaussian distribution are pointed out.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2013.833238