IDEAS home Printed from
   My bibliography  Save this article

Sinh-arcsinh distributions


  • M. C. Jones
  • Arthur Pewsey


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.

Suggested Citation

  • M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:761-780

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. McKeague, Ian W., 2015. "Central limit theorems under special relativity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 149-155.
    2. Jones, M.C., 2012. "Relationships between distributions with certain symmetries," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1737-1744.
    3. Arthur Pewsey & Toshihiro Abe, 2015. "The sinh-arcsinhed logistic family of distributions: properties and inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 573-594, June.
    4. Rainer Dyckerhoff & Christophe Ley & Davy Paindaveine, 2015. "Depth-based runs tests for bivariate central symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 917-941, October.
    5. Angelica Gianfreda & Derek Bunn, 2018. "A Stochastic Latent Moment Model for Electricity Price Formation," BEMPS - Bozen Economics & Management Paper Series BEMPS46, Faculty of Economics and Management at the Free University of Bozen.
    6. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    7. M. C. Jones & Arthur Pewsey, 2012. "Inverse Batschelet Distributions for Circular Data," Biometrics, The International Biometric Society, vol. 68(1), pages 183-193, March.
    8. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    9. 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.
    10. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    11. repec:eee:csdana:v:115:y:2017:i:c:p:250-266 is not listed on IDEAS
    12. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    13. 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.
    14. Rigby, Robert & Stasinopoulos, Dimitrios & Voudouris, Vlasios, 2015. "Flexible statistical models: Methods for the ordering and comparison of theoretical distributions," MPRA Paper 63620, University Library of Munich, Germany.
    15. Matsumoto, Ken'ichi & Voudouris, Vlasios & Stasinopoulos, Dimitrios & Rigby, Robert & Di Maio, Carlo, 2012. "Exploring crude oil production and export capacity of the OPEC Middle East countries," Energy Policy, Elsevier, vol. 48(C), pages 820-828.
    16. Djennad, Abdelmajid & Rigby, Robert & Stasinopoulos, Dimitrios & Voudouris, Vlasios & Eilers, Paul, 2015. "Beyond location and dispersion models: The Generalized Structural Time Series Model with Applications," MPRA Paper 62807, University Library of Munich, Germany.
    17. 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.
    18. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:761-780. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.