A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference


  • Neha Choudhary Ch. Charan Singh University
  • Abhishek Tyagi Ch. Charan Singh University
  • Bhupendra Singh Ch. Charan Singh University




Extended modified Weibull distribution, Maximum likelihood estimates, Bayesian estimates, Gibbs sampler, Tierney and Kadane's approximation, Highest posterior density intervals


In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.


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How to Cite

Choudhary, N., Tyagi, A., & Singh, B. (2021). A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference. Statistica, 81(1), 65–92. https://doi.org/10.6092/issn.1973-2201/10025