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A Family of Generalised Beta Distributions: Properties and Applications

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Listed:
  • Emilio Gómez-Déniz

    (University of Las Palmas de Gran Canaria)

  • José María Sarabia

    (University of Cantabria)

Abstract

A family of continuous distributions with bounded support, which is a generalisation of the standard beta distribution, is introduced. We study some basic properties of the new family and simulation experiments are performed to observe the behaviour of the maximum likelihood estimators. We also derive a multivariate version of the proposed distributions. Three numerical experiments were performed to determine the flexibility of the new family of distributions in comparison with other extensions of the beta distribution that have been proposed. In this respect, the new family was found to be superior.

Suggested Citation

  • Emilio Gómez-Déniz & José María Sarabia, 2018. "A Family of Generalised Beta Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 5(3), pages 401-420, September.
    • Handle: RePEc:spr:aodasc:v:5:y:2018:i:3:d:10.1007_s40745-018-0143-6
    DOI: 10.1007/s40745-018-0143-6
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    References listed on IDEAS

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    1. 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.
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    7. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    8. 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.
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