IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i8p2021-2034.html
   My bibliography  Save this article

A new skew generalization of the normal distribution: Properties and applications

Author

Listed:
  • García, V.J.
  • Gómez-Déniz, E.
  • Vázquez-Polo, F.J.

Abstract

A new class of distribution functions with not-necessarily symmetric densities, which contains the normal one as a particular case, is introduced. The class thus obtained depends on a set of three parameters, with an additional one to the classical normal distribution being inserted. This new class of skewed distributions is presented as an alternative to the class of skew-normal and Balakrishnan skew-normal distributions, among others. The density and distribution functions of this new class are given by a closed expression which allows us to easily compute probabilities, moments and related measurements. Certain interesting regularity properties reduce the study of this class to one of a subset of standardized distributions. Finally, some applications are shown as examples.

Suggested Citation

  • García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:8:p:2021-2034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00094-0
    Download Restriction: Full text for ScienceDirect subscribers only.

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

    References listed on IDEAS

    as
    1. Kundu, Debasis & Dey, Arabin Kumar, 2009. "Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 956-965, February.
    2. Ramesh Gupta & Rameshwar Gupta, 2004. "Generalized skew normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 501-524, December.
    3. Xie, Feng-Chang & Lin, Jin-Guan & Wei, Bo-Cheng, 2009. "Diagnostics for skew-normal nonlinear regression models with AR(1) errors," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4403-4416, October.
    4. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
    5. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    6. Leiva, Vctor & Sanhueza, Antonio & Kelmansky, Diana M. & Martnez, Elena J., 2009. "On the glog-normal distribution and its application to the gene expression problem," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1613-1621, March.
    7. Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
    8. K. Jayakumar & Thomas Mathew, 2008. "On a generalization to Marshall–Olkin scheme and its application to Burr type XII distribution," Statistical Papers, Springer, vol. 49(3), pages 421-439, July.
    9. Adelchi Azzalini & Monica Chiogna, 2004. "Some results on the stress–strength model for skew-normal variates," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 315-326.
    10. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400, September.
    11. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    12. repec:mes:challe:v:31:y:1988:i:4:p:56-58 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Teimouri, Mahdi & Nadarajah, Saralees, 2013. "On simulating Balakrishnan skew-normal variates," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 52-58.

    Corrections

    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:eee:csdana:v:54:y:2010:i:8:p:2021-2034. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.