On bivariate transformation of scale distributions |
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Authors: | MC Jones |
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Institution: | 1. Department of Mathematics &2. Statistics, The Open University, Milton Keynes, UKm.c.jones@open.ac.uk |
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Abstract: | ABSTRACTElsewhere, 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. |
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Keywords: | Bivariate inverse Gaussian distribution R-symmetry Sinh–arcsinh transformation Skew-symmetric distribution Two-piece distribution |
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