Bayesian modeling of bathtub shaped hazard rate using various Weibull extensions and related issues of model selection
 S. K. Upadhyay,
 Ashutosh Gupta,
 Dipak K. Dey
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Bathtub shape is one of the most important behaviors of the hazard rate function that is quite common in lifetime data analysis. Such shapes are actually the combination of three different shapes and, as such, there have been several proposals to model such behavior. One such proposal is to combine at most three different distributions, often the Weibull or some similar model, separately for decreasing, constant, and increasing shapes of the hazard rate. Sometimes combination of two different models may also result in the required bathtub shape. The other proposal includes generalizing or modifying the twoparameter distribution by adding an extra parameter into it. It is often seen that the first proposal is quite cumbersome whereas the second fails to capture some important aspects of the data. The present work considers two recent generalizations/modifications of the twoparameter Weibull model, namely the Weibull extension and the modified Weibull models, and proposes mixing the two families separately with the threeparameter Weibull distribution in order to see if the mixing results in some real benefit though at the cost of too many parameters. The paper finally considers the complete Bayes analysis of the proposed models using Markov chain Monte Carlo simulation and compares them with both Weibull extension and the modified Weibull models in a Bayesian framework. It is observed that the mixture models offer drastic improvement over the individual models not only in terms of hazard rate but also in terms of overall performance. The results are illustrated with the help of a real data based example.
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 Title
 Bayesian modeling of bathtub shaped hazard rate using various Weibull extensions and related issues of model selection
 Journal

Sankhya B
Volume 74, Issue 1 , pp 1543
 Cover Date
 20120501
 DOI
 10.1007/s1357101200414
 Print ISSN
 09768386
 Online ISSN
 09768394
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Primary 62F15
 Secondary 62N03, 62N05
 Bathtub shaped hazard rate, Weibull extension and modified Weibull models, Weibull model, mixture model, Markov chain Monte Carlo, data augmentation, BIC, DIC, Predictive simulation.
 Authors

 S. K. Upadhyay ^{(1)}
 Ashutosh Gupta ^{(2)}
 Dipak K. Dey ^{(3)}
 Author Affiliations

 1. Department of Statistics and DST Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, 221 005, India
 2. Biomedical Data Sciences, GlaxoSmithKline Pharmaceuticals Limited, Embassy Links 5, SRT Road, Bangalore, 560 052, India
 3. Department of Statistics, University of Connecticut, 215 Glenbrook Road, Unit 4098, Storrs, CT, 06269–4098, USA