IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v24y2015i3p359-372.html
   My bibliography  Save this article

A new method for adding two parameters to a family of distributions with application to the normal and exponential families

Author

Listed:
  • H. Barakat

Abstract

In this paper we introduce a new method to add two parameters to a family of distributions. Through the additional parameters we can fully control the skewness and kurtosis of the resulting family. This method is applied to yield a new two-parameter extension of the standard normal distribution, which may be positively–negatively asymmetric and leptokurtic–platykurtic. In addition, this method is applied to yield a new three-parameter extension of the exponential distribution, which may be symmetric and has non-constant hazard rate function. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • H. Barakat, 2015. "A new method for adding two parameters to a family of distributions with application to the normal and exponential families," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 359-372, September.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:3:p:359-372
    DOI: 10.1007/s10260-014-0265-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10260-014-0265-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10260-014-0265-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    2. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    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. Devendra Kumar & Manoj Kumar, 2019. "A New Generalization of the Extended Exponential Distribution with an Application," Annals of Data Science, Springer, vol. 6(3), pages 441-462, September.
    2. Gayan Warahena-Liyanage & Broderick Oluyede & Thatayaone Moakofi & Whatmore Sengweni, 2023. "The New Exponentiated Half Logistic-Harris-G Family of Distributions with Actuarial Measures and Applications," Stats, MDPI, vol. 6(3), pages 1-29, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    2. Fischer, Matthias J., 2004. "The L-distribution and skew generalizations," Discussion Papers 63/2004, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    3. Matthias Wagener & Andriette Bekker & Mohammad Arashi, 2021. "Mastering the Body and Tail Shape of a Distribution," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    4. A. Abtahi & M. Towhidi & J. Behboodian, 2011. "An appropriate empirical version of skew-normal density," Statistical Papers, Springer, vol. 52(2), pages 469-489, May.
    5. Fischer, Matthias J., 2006. "The L-distribution and skew generalizations," Discussion Papers 75/2006, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    6. Félix Belzunce & Julio Mulero & José María Ruíz & Alfonso Suárez-Llorens, 2015. "On relative skewness for multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 813-834, December.
    7. Mameli, Valentina, 2015. "The Kumaraswamy skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 75-81.
    8. Klein, Ingo, 2011. "Van Zwet ordering and the Ferreira-Steel family of skewed distributions," FAU Discussion Papers in Economics 13/2011, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    9. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    10. Devendra Kumar & Manoj Kumar, 2019. "A New Generalization of the Extended Exponential Distribution with an Application," Annals of Data Science, Springer, vol. 6(3), pages 441-462, September.
    11. 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.
    12. Fischer, Matthias J. & Vaughan, David, 2004. "The Beta-Hyperbolic Secant (BHS) Distribution," Discussion Papers 64/2004, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    13. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
    14. 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.
    15. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    16. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    17. Carol Alexander & José María Sarabia, 2012. "Quantile Uncertainty and Value‐at‐Risk Model Risk," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1293-1308, August.
    18. A. A. Ogunde & S. T. Fayose & B. Ajayi & D. O. Omosigho, 2020. "Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-90, November.
    19. Ghosh Indranil, 2019. "On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 115-121, December.
    20. Abdus Saboor & Muhammad Nauman Khan & Gauss M. Cordeiro & Marcelino A. R. Pascoa & Juliano Bortolini & Shahid Mubeen, 2019. "Modified beta modified-Weibull distribution," Computational Statistics, Springer, vol. 34(1), pages 173-199, March.

    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:spr:stmapp:v:24:y:2015:i:3:p:359-372. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.