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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bolstad, W.M.: Understanding Computational Bayesian Statistics. Wiley, New York (2010)
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)
Brooks, S.P., Gelman, A.: Alternative methods for monitoring convergence of iterative simulations. J. Comput. Graph. Stat. 7, 434–55 (1998)
Carlin, B.P., Louis, T.A.: Bayesian methods for data analysis. 3rd edn. CRC press, chapman and Hall, Boca Raton (2009)
Congdon, P.: Bayesian Statistical Modelling, 2nd edn. Wiley, New York (2006)
Gamerman, D.: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall, London (1997)
Gelfand, A.E., Smith, A.F.M.: Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398–409 (1990)
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)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian data analysis, 2nd edn. Chapman and Hill, NewYork (2003)
Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions and the bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–41 (1984)
Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)
Ibrahim, J.G., Chen, M.H., Sinha, D.: Bayesian Survival Analysis. Springer Inc, New York (2001)
Metropolis, N., Ulam, S.: The Monte Carlo method. J. Am. Stat. Assoc. 44(247), 335–41 (1949)
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)
Prop, J.G., Wilson, D.B.: Exact sampling with coupled markov chains and applications to statistical mechanics. Random Struct. Algorithms 9, 223–52 (1996)
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)
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)
Tanner, M.A., Wong, W.H.: The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82, 528–49 (1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Hanagal, D.D. (2019). Some Parametric Models. In: Modeling Survival Data Using Frailty Models. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-1181-3_2
Download citation
DOI: https://doi.org/10.1007/978-981-15-1181-3_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-1180-6
Online ISBN: 978-981-15-1181-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)