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Sinh-arcsinh distributions

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  • M. C. Jones
  • Arthur Pewsey
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    Abstract

    We introduce the sinh-arcsinh transformation and hence, by applying it to a generating distribution with no parameters other than location and scale, usually the normal, a new family of sinh-arcsinh distributions. This four-parameter family has symmetric and skewed members and allows for tailweights that are both heavier and lighter than those of the generating distribution. The central place of the normal distribution in this family affords likelihood ratio tests of normality that are superior to the state-of-the-art in normality testing because of the range of alternatives against which they are very powerful. Likelihood ratio tests of symmetry are also available and are very successful. Three-parameter symmetric and asymmetric subfamilies of the full family are also of interest. Heavy-tailed symmetric sinh-arcsinh distributions behave like Johnson S U distributions, while their light-tailed counterparts behave like sinh-normal distributions, the sinh-arcsinh family allowing a seamless transition between the two, via the normal, controlled by a single parameter. The sinh-arcsinh family is very tractable and many properties are explored. Likelihood inference is pursued, including an attractive reparameterization. Illustrative examples are given. A multivariate version is considered. Options and extensions are discussed. Copyright 2009, Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/biomet/asp053
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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 96 (2009)
    Issue (Month): 4 ()
    Pages: 761-780

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    Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:761-780

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    Cited by:
    1. Jones, M.C., 2012. "Relationships between distributions with certain symmetries," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1737-1744.
    2. Voudouris, Vlasios & Stasinopoulos, Dimitrios & Rigby, Robert & Di Maio, Carlo, 2011. "The ACEGES laboratory for energy policy: Exploring the production of crude oil," Energy Policy, Elsevier, vol. 39(9), pages 5480-5489, September.
    3. Ley, Christophe & Paindaveine, Davy, 2010. "Multivariate skewing mechanisms: A unified perspective based on the transformation approach," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1685-1694, December.
    4. Rubio, F.J. & Steel, M.F.J., 2012. "On the Marshall–Olkin transformation as a skewing mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2251-2257.

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