Bayesian Modelling of Exponentiated Weibull Generated Family for Interval-censored Data with rstan


  • Shazia Farhin Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, UP, India
  • Md Ashraf-Ul-Alam Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, UP, India
  • Athar Ali Khan Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, UP, India


Bayesian analysis, survival models, EW-generated family, interval censored data, LOO, R, Stan


The purpose of this paper is to fit the Exponentiated Weibull generated (EW-G) family to intervalcensored survival data in the Bayesian environment, which is an extended version of the Weibull-G family and generated by Exponentiated Weibull random variable. Based on the EW-G family, three special models, namely Exponentiated Weibull Exponential, Exponentiated Weibull Weibull, and Exponentiated Weibull Rayleigh are applied for the analysis. The models are fitted in R using the probabilistic programming language Stan, which offers full Bayesian inference through Hamiltonian Monte Carlo algorithm and their extension No-U-turn sampler algorithm. Stan codes for the analysis are provided. We compared the model with the leave-one-out-cross validation information criterion, and we found that simpler models with fewer parameters give a better fitting to the data.


AbuJarad MH, Khan AA. Bayesian survival analysis of Topp-Leone generalized family with Stan.

Int J Stat Appl. 2018; 8(5): 274-290.

AbuJarad MH, Khan AA, Khaleel MA, AbuJarad ES, AbuJarad AH, Oguntunde PE. Bayesian reliability analysis of Marshall and Olkin model. Ann Data Sci. 2020; 7(3): 461-489.

Akhtar MT, Khan AA. Bayesian analysis of generalized log-Burr family with R. SpringerPlus. 2014;

(1): 1-10.

Almetwaly EM, Almongy HM. Estimation of the generalized power Weibull distribution parameters

using progressive censoring schemes. Int J Probab Stat. 2018; 7(2): 51-61.

Bogaerts K, Komarek A, Lesaffre E. Survival analysis with interval-censored data: A practical ap- ´

proach with examples in R, SAS, and BUGS. Chapman and Hall/CRC; 2017.

Bourguignon M, Silva RB, Cordeiro GM. The Weibull-G family of probability distributions. J Data

Sci. 2014; 12(1): 53-68.

Collett D. Modelling survival data in medical research. CRC press; 2015.

Cordeiro GM, Afify AZ, Yousof HM, Pescim RR, Aryal GR. The exponentiated Weibull-H family of

distributions: Theory and Applications. Mediterr J Math. 2017; 14(4): 1-22.

Duane S, Kennedy AD, Pendleton BJ, Roweth D. Hybrid monte carlo. Phys Lett. B. 1987; 195(2):


Elgarhy M, Shakil M, Kibria G. Exponentiated Weibull-exponential distribution with applications.

Appl Appl Math. 2017; 12(2): 710-725.

Gelfand AE, Dey DK, Chang H. Model determination using predictive distributions with implementation via sampling-based methods. Stanford Univ CA Dept of Statistics; 1992.

Gelman A. Prior distributions for variance parameters in hierarchical models (comment on article by

Browne and Draper). Bayesian Anal. 2006; 1(3): 515-534.

Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. Chapman and Hall/CRC; 2013.

Hassan AS, Elgarhy M. A new family of exponentiated Weibull-generated distributions. Int. J. Math.

Appl. 2016; 4(1):135-148.

Hoffman MD, Gelman A. The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian

Monte Carlo J Mach Learn Res. 2014; 15(1): 1593-1623.

Khan N, Khan AA. Bayesian Analysis of Topp-Leone Generalized Exponential Distribution. Austrian

J Stat. 2018; 47(4): 1-15.

Mahmoud MAW, Ghazal MGM. Estimations from the exponentiated rayleigh distribution based on

generalized Type-II hybrid censored data. J Egyptian Math Soc. 2017; 25(1): 71-78.

McElreath R. Statistical rethinking: A Bayesian course with examples in R and Stan. Chapman and

Hall/CRC; 2018.

Mudholkar GS, Srivastava DK, Freimer M. The exponentiated Weibull family: A reanalysis of the

bus-motor-failure data. Technometrics. 1995; 37(4): 436-445.

R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical

Computing, Vienna, Austria. 2021. Available from:

Sindhu TN, Aslam M, Hussain Z. Bayesian estimation on the generalized logistic distribution under

left type-II censoring. Thail Stat. 2016; 14(2): 181-195.

Sindhu TN, Feroze N, Aslam M. A class of improved informative priors for bayesian analysis of

two-component mixture of failure time distributions from doubly censored data. J Stat Manage

Syst. 2017; 20(5): 871-900.

Sindhu TN, Hussain Z. Predictive inference and parameter estimation from the half-normal distribution for the left censored data. Ann Data Sci. 2020: 1-15.

Stan Development Team. RStan: the R interface to Stan. R package version 2.21.2. 2020. Available


Stan Development Team. Stan Modeling Language Users Guide and Reference Manual Version

17.0. 2017.

Vehtari A, Gelman A, Gabry J. Efficient implementation of leave-one-out cross-validation and WAIC

for evaluating fitted Bayesian models. arXiv preprint arXiv:1507.04544. 2015.

Vehtari A, Gelman A, Gabry J. Practical Bayesian model evaluation using leave-one-out crossvalidation and WAIC Stat. Comput. 2017; 27(5): 1413-1432.

Whitehead J. The analysis of relapse clinical trials, with application to a comparison of two ulcer

treatments. Stat Med. 1989; 8(12): 1439-1454.




How to Cite

Farhin, S. ., Ashraf-Ul-Alam, M. ., & Ali Khan, A. . (2023). Bayesian Modelling of Exponentiated Weibull Generated Family for Interval-censored Data with rstan. Thailand Statistician, 21(4), 783–801. Retrieved from