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Generalized beta-generated distributions

Author

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  • Alexander, Carol
  • Cordeiro, Gauss M.
  • Ortega, Edwin M.M.
  • Sarabia, José María

Abstract

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Suggested Citation

  • Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1880-1897 DOI: 10.1016/j.csda.2011.11.015
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    References listed on IDEAS

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    Cited by:

    1. repec:eee:reensy:v:124:y:2014:i:c:p:32-55 is not listed on IDEAS
    2. Mameli, Valentina, 2015. "The Kumaraswamy skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 75-81.
    3. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, Reading University.
    4. Ibrahim Elbatal & Francesca Condino & Filippo Domma, 2016. "Reflected Generalized Beta Inverse Weibull Distribution: definition and properties," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 316-340, November.
    5. Emanuela Ciapanna & Marco Taboga & Eliana Viviano, 2015. "Sectoral differences in managers’ compensation: insights from a matching model," Temi di discussione (Economic working papers) 1000, Bank of Italy, Economic Research and International Relations Area.
    6. repec:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0079-y is not listed on IDEAS
    7. repec:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0301-x is not listed on IDEAS
    8. Greselin, Francesca & Zitikis, Ricardas, 2015. "Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references," MPRA Paper 65892, University Library of Munich, Germany.
    9. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    10. repec:spr:opsear:v:54:y:2017:i:2:d:10.1007_s12597-016-0281-6 is not listed on IDEAS
    11. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    12. Beatriz R. Lanjoni & Edwin M. M. Ortega & Gauss M. Cordeiro, 2016. "Extended Burr XII Regression Models: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 203-224, March.
    13. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.

    More about this item

    Keywords

    Entropy; Exponentiated; Kumaraswamy; Kurtosis; McDonald; Minimax; Skewness;

    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

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