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Relationships between distributions with certain symmetries


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  • Jones, M.C.
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    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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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 9 ()
    Pages: 1737-1744

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1737-1744

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    Keywords: Birnbaum–Saunders distribution; Inverse Gaussian distribution; R-symmetry; Random variate generation; Skew-symmetric distribution;


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    1. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    2. M.C. Jones, 2007. "Connecting Distributions with Power Tails on the Real Line, the Half Line and the Interval," International Statistical Review, International Statistical Institute, vol. 75(1), pages 58-69, 04.
    3. Ramesh C. Gupta & Debasis Kundu, 2011. "Weighted inverse Gaussian -- a versatile lifetime model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2695-2708, February.
    4. Antonio Sanhueza & Víctor Leiva & N. Balakrishnan, 2008. "A new class of inverse Gaussian type distributions," Metrika, Springer, vol. 68(1), pages 31-49, June.
    5. J. Rosco & M. Jones & Arthur Pewsey, 2011. "Skew t distributions via the sinh-arcsinh transformation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 20(3), pages 630-652, November.
    6. Víctor Leiva & Hugo Hernández & Antonio Sanhueza, . "An R Package for a General Class of Inverse Gaussian Distributions," Journal of Statistical Software, American Statistical Association, vol. 26(i04).
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    Cited by:
    1. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.


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