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On bivariate transformation of scale distributions

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  • M.C. Jones

Abstract

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.

Suggested Citation

  • M.C. Jones, 2016. "On bivariate transformation of scale distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 577-588, February.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:3:p:577-588
    DOI: 10.1080/03610926.2013.833238
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    Cited by:

    1. Jonas Baillien & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible asymmetric multivariate distributions based on two-piece univariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 159-200, February.

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