IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2011-05.html
   My bibliography  Save this paper

Generalized Beta-Generated Distributions

Author

Listed:
  • Carol Alexander

    (ICMA Centre, Henley Business School, University of Reading)

  • Gauss M. Cordeiro

    (Departamento de Estatística, Universidade Federal de Pernambuco, Brazil)

  • Edwin M. M. Ortega

    (Departamento de Ciências Exatas, Universidade de São Paulo, Brazil)

  • José María Sarabia

    (Department of Economics, University of Cantabria, Spain)

Abstract

This paper introduces a new class of generalized beta-generated distributions that have very flexible shapes and tractable properties. Their quantiles and moments have a simple closed form and they are maximum entropy distributions under three simple conditions. Two special cases are the classical beta-generated and the Kumaraswamy-generated distributions. An attractive feature of generalized beta-normal distributions is that the three generalized beta parameters afford greater control over the weights in both tails and in the centre of the generated distribution, compared with the classical beta-normal distribution.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Carol Alexander & Gauss M. Cordeiro & Edwin M. M. Ortega & José María Sarabia, 2011. "Generalized Beta-Generated Distributions," ICMA Centre Discussion Papers in Finance icma-dp2011-05, Henley Business School, University of Reading.
  • Handle: RePEc:rdg:icmadp:icma-dp2011-05
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/files/discussion-papers/DP2011-05.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    2. 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.
    3. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
    4. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    5. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    6. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    7. Brys, Guy & Hubert, Mia & Struyf, Anja, 2006. "Robust measures of tail weight," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 733-759, February.
    8. Nadarajah, Saralees & Gupta, Arjun K., 2007. "A generalized gamma distribution with application to drought data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 1-7.
    9. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose Maria, 2006. "Families of Multivariate Distributions Involving the Rosenblatt Construction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1652-1662, December.
    10. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
    11. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
    12. Amit Choudhury, 2005. "A Simple Derivation of Moments of the Exponentiated Weibull Distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 17-22, September.
    13. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    14. M. C. Jones & P. V. Larsen, 2004. "Multivariate distributions with support above the diagonal," Biometrika, Biometrika Trust, vol. 91(4), pages 975-986, December.
    15. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    16. Ebrahimi, Nader & Maasoumi, Esfandiar & Soofi, Ehsan S., 1999. "Ordering univariate distributions by entropy and variance," Journal of Econometrics, Elsevier, vol. 90(2), pages 317-336, June.
    17. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    Full references (including those not matched with items on IDEAS)

    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. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    2. Dongming Zhu & John W. Galbraith, 2009. "Forecasting Expected Shortfall with a Generalized Asymmetric Student-t Distribution," CIRANO Working Papers 2009s-24, CIRANO.
    3. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.
    4. Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.
    5. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    6. Allen, David & Lizieri, Colin & Satchell, Stephen, 2020. "A comparison of non-Gaussian VaR estimation and portfolio construction techniques," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 356-368.
    7. Zhu, Dongming & Galbraith, John W., 2010. "A generalized asymmetric Student-t distribution with application to financial econometrics," Journal of Econometrics, Elsevier, vol. 157(2), pages 297-305, August.
    8. Ibrahim Ergen, 2015. "Two-step methods in VaR prediction and the importance of fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1013-1030, June.
    9. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    10. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    11. Rubio, Francisco Javier & Steel, Mark F. J., 2014. "Bayesian modelling of skewness and kurtosis with two-piece scale and shape transformations," MPRA Paper 57102, University Library of Munich, Germany.
    12. 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.
    13. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    14. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    15. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    16. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    17. Alfonso Novales & Laura Garcia-Jorcano, 2019. "Backtesting Extreme Value Theory models of expected shortfall," Documentos de Trabajo del ICAE 2019-24, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    18. James B. McDonald & Daniel B. Walton & Bryan Chia, 2020. "Distributional Assumptions and the Estimation of Contingent Valuation Models," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 431-460, August.
    19. Toshinao Yoshiba, 2013. "Risk Aggregation by a Copula with a Stressed Condition," Bank of Japan Working Paper Series 13-E-12, Bank of Japan.
    20. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, University of Reading.

    More about this item

    Keywords

    Beta; Distribution; Entropy; Estimation; Exponentiated; Gamma; Generalized; Generated; Gumbel; Inverse Guassian; Kumaraswamy; Kurtosis; Laplace; McDonald; Minimax; MLE; MGF; Reliability; Skewness; Weibull.;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G1 - Financial Economics - - General Financial Markets

    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:rdg:icmadp:icma-dp2011-05. 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: Marie Pearson (email available below). General contact details of provider: https://edirc.repec.org/data/bsrdguk.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.