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The beta Burr XII distribution with application to lifetime data

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  • Paranaíba, Patrícia F.
  • Ortega, Edwin M.M.
  • Cordeiro, Gauss M.
  • Pescim, Rodrigo R.

Abstract

For the first time, a five-parameter distribution, the so-called beta Burr XII distribution, is defined and investigated. The new distribution contains as special sub-models some well-known distributions discussed in the literature, such as the logistic, Weibull and Burr XII distributions, among several others. We derive its moment generating function. We obtain, as a special case, the moment generating function of the Burr XII distribution, which seems to be a new result. Moments, mean deviations, Bonferroni and Lorenz curves and reliability are provided. We derive two representations for the moments of the order statistics. The method of maximum likelihood and a Bayesian analysis are proposed for estimating the model parameters. The observed information matrix is obtained. For different parameter settings and sample sizes, various simulation studies are performed and compared in order to study the performance of the new distribution. An application to real data demonstrates that the new distribution can provide a better fit than other classical models. We hope that this generalization may attract wider applications in reliability, biology and lifetime data analysis.

Suggested Citation

  • Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1118-1136
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    References listed on IDEAS

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    5. 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.
    6. Shao, Quanxi, 2004. "Notes on maximum likelihood estimation for the three-parameter Burr XII distribution," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 675-687, April.
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    Cited by:

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    3. Nadarajah, Saralees & Rocha, Ricardo, 2016. "Newdistns: An R Package for New Families of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i10).
    4. Chakraburty Subrata & Alizadeh Morad & Handique Laba & Altun Emrah & Hamedani G. G., 2021. "A new extension of Odd Half-Cauchy Family of Distributions: properties and applications with regression modeling," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 77-100, December.
    5. Mahmoudi, Eisa, 2011. "The beta generalized Pareto distribution with application to lifetime data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2414-2430.
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    7. Joyce, Paul & Abdo, Zaid, 2018. "Determining the distribution of fitness effects using a generalized Beta-Burr distribution," Theoretical Population Biology, Elsevier, vol. 122(C), pages 88-96.
    8. Renata Rojas Guerra & Fernando A. Peña-Ramírez & Gauss M. Cordeiro, 2023. "The Logistic Burr XII Distribution: Properties and Applications to Income Data," Stats, MDPI, vol. 6(4), pages 1-20, November.
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    10. Singh, Vijay P., 2018. "Systems of frequency distributions for water and environmental engineering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 50-74.
    11. Lucas D. Ribeiro Reis & Gauss M. Cordeiro & Maria do Carmo S. Lima, 2022. "The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data," Stats, MDPI, vol. 5(1), pages 1-43, March.
    12. 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.
    13. Hanieh Panahi, 2019. "Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 510-518, August.
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