Relationships between distributions with certain symmetries
The genesis of two-way links between the inverse Gaussian and Birnbaum–Saunders distributions is explored and extended. The most general results apply to pairs of distributions with a general ‘S-symmetry’ structure involving a self-inverse function closely related to a transformation function with certain properties. These general results arise by transformation from very simple properties of the familiar Azzalini-type skew-symmetric distributions. They specialise again to relationships between R-symmetric and log-symmetric distributions, between various models related to the inverse Gaussian and Birnbaum–Saunders distributions, relationships involving the sinh–arcsinh transformation, and others. Simple random variate generation is a practical consequence of these relationships.
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Volume (Year): 82 (2012)
Issue (Month): 9 ()
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- Antonio Sanhueza & Víctor Leiva & N. Balakrishnan, 2008. "A new class of inverse Gaussian type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 31-49, June.
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