IDEAS home Printed from https://ideas.repec.org/p/zbw/faucse/642004.html
   My bibliography  Save this paper

The Beta-Hyperbolic Secant (BHS) Distribution

Author

Listed:
  • Fischer, Matthias J.
  • Vaughan, David

Abstract

The shape of a probability distribution is often summarized by the distribution's skewness and kurtosis. Starting from a symmetric parent density f on the real line, we can modify its shape (i.e. introduce skewness and in-/decrease kurtosis) if f is appropriately weighted. In particular, every density w on the interval (0; 1) is a specific weighting function. Within this work, we follow up a proposal of Jones (2004) and choose the Beta distribution as underlying weighting function w. Parent distributions like the Student-t, the logistic and the normal distribution have already been investigated in the literature. Based on the assumption that f is the density of a hyperbolic secant distribution, we introduce the Beta-hyperbolic secant (BHS) distribution. In contrast to the Beta-normal distribution and the to Beta-Student-t distribution, BHS densities are always unimodal and all moments exist. In contrast to the Beta-logistic distribution, the BHS distribution is more êexible regarding the range of skewness and leptokurtosis combinations. Moreover, we propose a generalization which nests both the Beta-logistic and the BHS distribution. Finally, the goodness-of-fit between all above-mentioned distributions is compared for glass fibre data and aluminium returns.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:faucse:642004
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/29617/1/614047706.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    3. 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.
    4. 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. Wolfgang Kössler & Janine Ott, 2019. "Two-sided variable inspection plans for arbitrary continuous populations with unknown distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 437-452, September.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Klein, Ingo & Fischer, Matthias J., 2003. "Skewness by splitting the scale parameter," Discussion Papers 55/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    6. Fischer, Matthias J., 2004. "The L-distribution and skew generalizations," Discussion Papers 63/2004, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    7. 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.
    8. José María Sarabia & Faustino Prieto & Vanesa Jordá & Stefan Sperlich, 2020. "A Note on Combining Machine Learning with Statistical Modeling for Financial Data Analysis," Risks, MDPI, vol. 8(2), pages 1-14, April.
    9. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    10. Sanku Dey & Vikas Kumar Sharma & Mhamed Mesfioui, 2017. "A New Extension of Weibull Distribution with Application to Lifetime Data," Annals of Data Science, Springer, vol. 4(1), pages 31-61, March.
    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. 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.
    13. 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;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 630-652, November.
    14. Lyu, Yongjian & Wang, Peng & Wei, Yu & Ke, Rui, 2017. "Forecasting the VaR of crude oil market: Do alternative distributions help?," Energy Economics, Elsevier, vol. 66(C), pages 523-534.
    15. Mavis Pararai & Broderick O. Oluyede & Gayan Warahena-Liyanage, 2016. "The Beta Lindley-Poisson Distribution with Applications," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 5(4), pages 1-1.
    16. 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.
    17. Hasanov, Akram Shavkatovich & Poon, Wai Ching & Al-Freedi, Ajab & Heng, Zin Yau, 2018. "Forecasting volatility in the biofuel feedstock markets in the presence of structural breaks: A comparison of alternative distribution functions," Energy Economics, Elsevier, vol. 70(C), pages 307-333.
    18. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa Ç. Korkmaz & Munir Ahmad, 2018. "The transmuted geometric-quadratic hazard rate distribution: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-23, December.
    19. 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.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:zbw:faucse:642004. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/vierlde.html .

    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.