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Modeling the presence of immunes by using the exponentiated-Weibull model

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  • Vicente Cancho
  • Heleno Bolfarine

Abstract

In this paper the exponentiated-Weibull model is modified to model the possibility that long-term survivors are present in the data. The modification leads to an exponentiated-Weibull mixture model which encompasses as special cases the exponential and Weibull mixture models typically used to model such data. Inference for the model parameters is considered via maximum likelihood and also via Bayesian inference by using Markov chain Monte Carlo simulation. Model comparison is considered by using likelihood ratio statistics and also the pseudo Bayes factor, which can be computed by using the generated samples. An example of a data set is considered for which the exponentiated-Weibull mixture model presents a better fit than the Weibull mixture model. Results of simulation studies are also reported, which show that the likelihood ratio statistics seems to be somewhat deficient for small and moderate sample sizes.

Suggested Citation

  • Vicente Cancho & Heleno Bolfarine, 2001. "Modeling the presence of immunes by using the exponentiated-Weibull model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 659-671.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:6:p:659-671
    DOI: 10.1080/02664760120059200
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    Cited by:

    1. Nandini Kannan & Debasis Kundu & P. Nair & R. C. Tripathi, 2010. "The generalized exponential cure rate model with covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1625-1636.
    2. Vicente G. Cancho & Dipak K. Dey & Francisco Louzada, 2016. "Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 572-584, March.
    3. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    4. Jorge Alberto Achcar & Em�lio Augusto Coelho-Barros & Josmar Mazucheli, 2013. "Block and Basu bivariate lifetime distribution in the presence of cure fraction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1864-1874, September.

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