View More View Less
  • 1 Departamento de Estatística, Universidade Federal de Pernambuco-UFPE, Recife, Brazil
  • | 2 UTFPR, Departamento de Matemática, Universidade Tecnológica Federal do Paraná, Apucarana, Brazil
  • | 3 ESALQ, Departamento de Ciências Exatas, Universidade de São Paulo-USP, Piracicaba, Brazil
  • | 4 Departamento de Estatística, Universidade Estadual de Londrina, Londrina, Brazil
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

We define the extended beta family of distributions to generalize the beta generator pioneered by Eugene et al. [10]. This paper is cited in at least 970 scientific articles and extends more than fifty well-known distributions. Any continuous distribution can be generalized by means of this family. The proposed family can present greater flexibility to model skewed data. Some of its mathematical properties are investigated and maximum likelihood is adopted to estimate its parameters. Further, for different parameter settings and sample sizes, some simulations are conducted. The superiority of the proposed family is illustrated by means of two real data sets.

  • [1]

    Alexander, C., Cordeiro, G. M., Ortega, E. M. M. and Sarabia, J. M., Generalized beta-generated distributions, Computational Statistics and Data Analysis, 56 (2012), 18801897.

    • Search Google Scholar
    • Export Citation
  • [2]

    Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseinl, B., Ortega, E. M. M. and Altun, E., The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation, 87 (2017), 908932.

    • Search Google Scholar
    • Export Citation
  • [3]

    Cordeiro, G. M., Afify, A. Z., Ortega, E. M. M., Suzuki, A. K. and Mead, M. E., The odd Lomax generator of distributions: Properties, estimation and applications, Journal of Computational and Applied Mathematics, 347 (2018), 222237.

    • Search Google Scholar
    • Export Citation
  • [4]

    Chaudhry, M. A., Qadir, A., Rafique, M. and Zubair, S. M., Extension of Euler’s beta function, Journal of Computational and Applied Mathematics, 78 (1997), 1932.

    • Search Google Scholar
    • Export Citation
  • [5]

    Chaudhry, M. A. and Zubair, S. M., On A Class of Incomplete Gamma Fnctions with Applications, Chapman and Hall, CRC Press, 2002.

  • [6]

    Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions, Dordrecht, Holland/Boston, U.S.: Reidel Publishing Company, 1974.

    • Search Google Scholar
    • Export Citation
  • [7]

    Cordeiro, G. M. and de Castro, M., A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81 (2011), 883898.

    • Search Google Scholar
    • Export Citation
  • [8]

    Cordeiro, G. M., Cintra, R. J., Rego, L. C. and Ortega, E. M. M., The McDonald normal distribution, Pakistan Journal of Statistics and Operations Research, 8 (2012), 301329.

    • Search Google Scholar
    • Export Citation
  • [9]

    del Aguila, J. S., Heiffig-del Aguila, L. S., Sasaki, F. F., Tsumanuma, G. M., Ongarelli, M. G., Spoto, M. H. F., Jacomino, A. P., Ortega, E. M. M. and Kluge, R. A., Postharvest modifications of mechanically injured bananas, Revista Iberoamericana de Tecnologia Postcosecha, 10 (2010), 7385.

    • Search Google Scholar
    • Export Citation
  • [10]

    Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications, Communications in Statistics–Theory and Methods, 31 (2002), 497512.

    • Search Google Scholar
    • Export Citation
  • [11]

    Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, 6th edition, Academic Press, San Diego, 2000.

  • [12]

    Gilchrist, W., Statistical modelling with quantile functions, Chapman and Hall, CRC Press, 2000.

  • [13]

    Greenacre, M. J., Theory and applications of correspondence analysis, Academic Press, London, 1984.

  • [14]

    Malhotra, N. K., Pesquisa de Marketing: uma orientação aplicada, Bookman, Porto Alegre, 2006.

  • [15]

    Paranaíba, P. F., Ortega, E. M. M., Cordeiro, G. M. and Pescim, R. R., The beta Burr XII distribution with application to lifetime data, Computational Statistics and Data Analysis, 55 (2011), 11181136.

    • Search Google Scholar
    • Export Citation
  • [16]

    Pescim, R. R., Cordeiro, G. M., Demétrio, C. G. B., Ortega, E. M. M. and Nadarajah, S., The new class of Kummer beta generalized distributions. Statistics and Operations Research Transactions, 36 (2012), 153180.

    • Search Google Scholar
    • Export Citation
  • [17]

    Pescim, R. R., Demétrio, C. G. B., Cordeiro, G. M., Ortega, E. M. M. and Urbano, M. R., The beta generalized half-normal distribution, Computational Statistics and Data Analysis, 54 (2010), 945957.

    • Search Google Scholar
    • Export Citation
  • [18]

    Ramires, T. G., Ortega, E. M. M., Cordeiro, G. M. and Hamedani, G. G., The beta generalized half-normal geometric distribution. Studia Scientiarum Mathematicarum Hungarica, 50 (2013), 523554.

    • Search Google Scholar
    • Export Citation
  • [19]

    Ramires, T. G., Ortega, E. M. M., Cordeiro, G. M. and Hens, N., A bimodal flexible distribution for lifetime data, Journal of Statistical Computation and Simulation, 86 (2016), 24502470.

    • Search Google Scholar
    • Export Citation
  • [20]

    Steinbrecher, G. and Shaw, W. T., Quantile mechanics, European Journal of Applied Mathmatics, 19 (2008), 87112.