Journal of Statistical Theory and Practice

, Volume 12, Issue 2, pp 397–411 | Cite as

On testing the fit of accelerated failure time and proportional hazard Weibull extension models

  • Nacira Seddik-AmeurEmail author
  • Wafa Treidi


Characterized by three parameters, the Weibull extension distribution is introduced by Xie et al. as a generalization of the classical Weibull distribution. In this article, we are interested in the construction of modified chi-squared goodness-of-fit tests for both an accelerated failure time and Cox proportional hazards models with the Weibull extension distribution as the baseline distribution. We use the technique introduced by Bagdonavicius and Nikulin for right-censored samples. Besides an important simulation study, the obtained results are applied to illustrative examples from real data sets.


Accelerated failure time models censored data chi-squared test Cox proportional hazards model maximum likelihood estimation 

AMS Subject Classification

60E15 62F03 62F12 62G05 


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  1. Aidi, K., and N. Seddik-Ameur. 2016. Chi-square tests for generalized exponential AFT distributions with censored data. Electronic Journal of Applied Statistical Analysis 9 (2):371–84.MathSciNetGoogle Scholar
  2. Bagdonavičius, V., R. J. Levuliene, and M. Nikulin. 2013. Chi-squared goodness-of-fit tests for parametric accelerated failure time models. Communications in Statistics—Theory and Methods 42 (15):2768–85. doi:10.1080/03610926.2011.617483.MathSciNetCrossRefGoogle Scholar
  3. Bagdonavičius, V., and M. Nikulin. 2011. Chi-squared goodness-of-fit test for right censored data. International Journal of Applied Mathematics and Statistics 24:30–50.MathSciNetGoogle Scholar
  4. Chouia, S., and N. Seddik-Ameur. 2017. A modified chi-square test for Bertholon model with censored data. Communications in Statistics-Simulation and Computation 46 (1):593–602. doi:10.1080/03610918.2014.972519.MathSciNetCrossRefGoogle Scholar
  5. Cox, D. R. 1972. Regression models and life table (with discussion). Journal of the Royal Statistical Society, Series B 34:187–202.MathSciNetzbMATHGoogle Scholar
  6. Cox, D. R., and D. Oakes. 1984. Analysis of survival data. Monographs on Statistics and Applied Probabilities. New York, NY: Chapman & Hall/CRC.Google Scholar
  7. Freireich, E. J., E. Gehan, E. Frei, L. R. Schroeder, I. J. Wolman, R. Anbari, E. O. Burgert, S. D. Mills, D. Pinkel, and O. S. Selawry. 1963. The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: A model for evaluation of other potentially useful therapy. Blood 21 (6):699–716.Google Scholar
  8. Goual, H., and N. Seddik-Ameur. 2014. Chi-square type test for the AFT- generalized inverse Weibull distribution. Communications in statistics-Theory and Methods 43:2605–17. doi:10.1080/03610926.2013.839043.MathSciNetCrossRefGoogle Scholar
  9. Gupta, A., B. Mukherjee, and S. K. Upadhyay. 2008. Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation. Reliability Engineering & System Safety 93:1434–43. doi:10.1016/j.ress.2007.10.008.CrossRefGoogle Scholar
  10. Lawless, J. F. 2003. Statistical models and methods for lifetime data. 2nd ed. New York: John Wiley.zbMATHGoogle Scholar
  11. Nardi, A., and M. Schemper. 2003. Comparing Cox and parametric models in clinical studies. Statistics in Medicine 22:3597–610. doi:10.1002/(ISSN)1097-0258.CrossRefGoogle Scholar
  12. Nelson, W. 1990. Accelerated life testing: Statistical models, data analysis and test plans. New York, NY: John Wiley and Sons.CrossRefGoogle Scholar
  13. Nikulin, N. S., and X. Q. Tran. 2014. On chi-squared testing in accelerated trials. International Journal of Performability Engineering 10 (1):53–62.Google Scholar
  14. Orbe, J., E. Ferreira, and V. Nunez-Anton. 2002. Comparing proportional hazards and accelerated failure time models for survival analysis. Statistics in Medicine 21:3493–510. doi:10.1002/sim.1251.CrossRefGoogle Scholar
  15. Ortega, E. M. M., V. G. Cancho, and G. A. Paula. 2009. Generalized log-gamma regression models with cure fraction. Lifetime Data Analysis 15:79–106. doi:10.1007/s10985-008-9096-y.MathSciNetCrossRefGoogle Scholar
  16. Ravi, V., and P. D. Gilbert. 2009. BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function. Journal Statist Software 32 (4):1–26.Google Scholar
  17. Smith, R. M., and L. J. Bain. 1975. An exponential power life-testing distribution. Communication in Statistics 4:469–81. doi:10.1080/03610927508827263.CrossRefGoogle Scholar
  18. Treidi, W., and N. Seddik-Ameur. 2016. NRR statistic for the extension Weibull distribution. Global Journal of Pure and Applied Mathematics 12 (4):2809–18.Google Scholar
  19. Voinov, V., M. Nikulin, and N. Balakrishnan. 2013. Chi-squared goodness of fit tests with applications, 256. New York, NY: Academic Press, Elsevier.zbMATHGoogle Scholar
  20. Xie, M., T. N. Goh, and Y. Tang. 2004. On changing points of mean residual life and failure rate function for some generalized Weibull distributions. Reliability Engineering and System Safety 84:293–99. Elsevier doi:10.1016/j.ress.2003.12.005.CrossRefGoogle Scholar
  21. Xie, M., Y. Tang, and T. N. Goh. 2002. A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering and System Safety 76:279–85. doi:10.1016/S0951-8320(02) 00022-4.CrossRefGoogle Scholar

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© Grace Scientific Publishing, 20 Middlefield Ct, Greensboro, NC 27455 2018

Authors and Affiliations

  1. 1.Laboratory of Probability and Statistics (LaPS)Badji Mokhtar UniversityAnnabaAlgeria

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