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Some Parametric Models

  • David D. HanagalEmail author
Chapter
Part of the Industrial and Applied Mathematics book series (INAMA)

Abstract

There are a handful of parametric models that have successfully served as population models for failure times. Sometimes there are probabilistic arguments based on the physics of the failure mode that tend to justify the choice of model. Sometimes the model is used solely because of its empirical success in fitting the actual failure data.

References

  1. Bolstad, W.M.: Understanding Computational Bayesian Statistics. Wiley, New York (2010)Google Scholar
  2. Bolstad, W.M., Manda, S.O.: Investigating child mortality in Malawi using family and community random effects: a Bayesian analysis. J. Am. Stat. Assoc. 96, 12 (2001)MathSciNetCrossRefGoogle Scholar
  3. Brooks, S.P., Gelman, A.: Alternative methods for monitoring convergence of iterative simulations. J. Comput. Graph. Stat. 7, 434–55 (1998)Google Scholar
  4. Carlin, B.P., Louis, T.A.: Bayesian methods for data analysis. 3rd edn. CRC press, chapman and Hall, Boca Raton (2009)Google Scholar
  5. Congdon, P.: Bayesian Statistical Modelling, 2nd edn. Wiley, New York (2006)Google Scholar
  6. Gamerman, D.: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall, London (1997)Google Scholar
  7. Gelfand, A.E., Smith, A.F.M.: Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398–409 (1990)MathSciNetCrossRefGoogle Scholar
  8. Gelman, A., Rubin, D.B.: A single series from the Gibbs sampler provides a false sense of security. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M., (eds.), Bayesian Statistics, vol. 4, pp. 625–632. Oxford University Press, Oxford (1992)Google Scholar
  9. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian data analysis, 2nd edn. Chapman and Hill, NewYork (2003)Google Scholar
  10. Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions and the bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–41 (1984)CrossRefGoogle Scholar
  11. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)MathSciNetCrossRefGoogle Scholar
  12. Ibrahim, J.G., Chen, M.H., Sinha, D.: Bayesian Survival Analysis. Springer Inc, New York (2001)CrossRefGoogle Scholar
  13. Metropolis, N., Ulam, S.: The Monte Carlo method. J. Am. Stat. Assoc. 44(247), 335–41 (1949)CrossRefGoogle Scholar
  14. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of state calculations by fast computing machine. J. Chem. Phys. 21, 1087–91 (1953)CrossRefGoogle Scholar
  15. Prop, J.G., Wilson, D.B.: Exact sampling with coupled markov chains and applications to statistical mechanics. Random Struct. Algorithms 9, 223–52 (1996)MathSciNetCrossRefGoogle Scholar
  16. Sahu, S.K., Dey, D.K., Aslanidou, H., Sinha, D.: A Weibull regression model with gamma frailties for multivariate survival data. Life Time Data Anal. 3, 123–137 (1997)CrossRefGoogle Scholar
  17. Santos, C.A., Achcar, J.A.: A Bayesian analysis for multivariate survival data in the presence of covariates. Jr. Stat. Theor. Appl. 9, 233–253 (2010)Google Scholar
  18. Tanner, M.A., Wong, W.H.: The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82, 528–49 (1987)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Symbiosis Statistical InstituteSymbiosis International UniversityPuneIndia

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