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Extended Burr XII Regression Models: Theory and Applications

Author

Listed:
  • Beatriz R. Lanjoni

    (Universidade de São Paulo)

  • Edwin M. M. Ortega

    (Universidade de São Paulo)

  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco, Cidade Universitária)

Abstract

We introduce two new lifetime distributions by compounding the Burr XII (BXII) and geometric distributions. We derive their moments and moment-generating and quantile functions. We also define two new extended regression models based on the logarithms of these distributions. The regression models are very useful in the analysis of real data since they can provide better fits than other special regression models. We formulate a new cure rate survival model, where the number of competing causes of the event of interest follows a geometric distribution and the time to this event has the BXII geometric distribution. The estimation of the model parameters is performed by maximum likelihood. We illustrate the importance of the new models by means of two real datasets. The first dataset comes from a study carried out at the Department of Entomology of the Luiz de Queiroz School of Agriculture, University of São Paulo, which aims to assess the longevity of the Mediterranean fruit fly (ceratitis capitata). The second dataset comes from the area of biology.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:1:d:10.1007_s13253-015-0236-z
    DOI: 10.1007/s13253-015-0236-z
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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.
    2. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    3. Giovana O. Silva & Edwin M.M. Ortega & Gilberto A. Paula, 2011. "Residuals for log-Burr XII regression models in survival analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1435-1445, June.
    4. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    5. Tsodikov A.D. & Ibrahim J.G. & Yakovlev A.Y., 2003. "Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1063-1078, January.
    6. Cooner, Freda & Banerjee, Sudipto & Carlin, Bradley P. & Sinha, Debajyoti, 2007. "Flexible Cure Rate Modeling Under Latent Activation Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 560-572, June.
    7. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.
    8. Silva, Giovana Oliveira & Ortega, Edwin M.M. & Cancho, Vicente G. & Barreto, Mauricio Lima, 2008. "Log-Burr XII regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3820-3842, March.
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    Cited by:

    1. Thiago G. Ramires & Niel Hens & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model," Computational Statistics, Springer, vol. 33(2), pages 709-730, June.
    2. Muhammad Zubair & Muhammad H. Tahir & Gauss M. Cordeiro & Ayman Alzaatreh & Edwin M. M. Ortega, 2018. "The power-Cauchy negative-binomial: properties and regression," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-17, December.

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