A Random Effects Model for Multivariate Life Data
Chapter
Abstract
The Weibull distribution is a natural starting point in the modelling of failure times and material strength data. In recent years there has been a growing interest in the modelling of heterogeneity within this context. A natural approach is to consider a mixture, either discrete or continuous, of Weibull distributions. A judicious choice of mixing distribution can lead to a tractable and flexible generalization of the Weibull distribution. An example is the Burr distribution, which is a gamma mixture of Weibull distributions, and this is used in the paper to illustrate the approach. Some relevant statistical methods are introduced and various applications are discussed.
Keywords
Random Effect Model Weibull Distribution Failure Time Weibull Model Covariate Information
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- Brindley, E.C. and Thompson, W.A. (1972), “Dependence and Ageing Aspects of Multi- variate Survival,” Journal of the American Statistical Association, 67, 822–830.MathSciNetMATHCrossRefGoogle Scholar
- Burr, I.W. (1942), “Cumulative Frequency Functions,” Annals of Mathematical Statistics, 13, 215–232.MathSciNetMATHCrossRefGoogle Scholar
- Clayton, D. (1978), “A Model for Association in Bivariate Life Tables and its Application in Epidemiological Studies of Familial Tendency in Chronic Disease Incidence” Biometrika, 65, 141–151.MathSciNetMATHCrossRefGoogle Scholar
- Crowder, M.J. (1985), “A Distributional Model for Repeated Failure Time Measurements,” Journal of the Royal Statistical Society B, 47, 447–452.MathSciNetGoogle Scholar
- Crowder, M.J. (1989), “A Multivariate Distribution with Weibull Connections,” Journal of the Royal Statistical Society B, 51, 93–107.MathSciNetMATHGoogle Scholar
- Crowder, M.J. and Kimber, A.C. (1994), “A Score Test for the Multivariate Burr and Other Weibull Mixture Distributions,” Submitted for publication.Google Scholar
- Crowder, M.J., Kimber, A.C., Smith, R.L. and Sweeting, T.J. (1991), Statistical Analysis of Reliability Data. London: Chapman and Hall.Google Scholar
- Everitt, B.S. and Hand, D.J. (1981), Finite Mixture Distributions. London: Chapman and Hall.MATHCrossRefGoogle Scholar
- Hougaard, P. (1984), “Life Table Methods for Heterogeneous Populations: Distributions Describing the Heterogeneity,” Biometrika, 71, 75–83.MathSciNetMATHCrossRefGoogle Scholar
- Hougaard, P. (1986a), “Survival Models for Heterogeneous Populations Derived from Stable Distributions,” Biometrika, 73, 387–396.MathSciNetMATHCrossRefGoogle Scholar
- Hougaard, P. (1986b), “A Class of Multivariate Failure Time Distributions,” Biometrika, 73, 671–678.MathSciNetMATHGoogle Scholar
- Hougaard, P. (1987), “Modelling Multivariate Survival,” Scandinavian Journal of Statistics, 14, 291–304.MathSciNetMATHGoogle Scholar
- Hougaard, P. (1991), “Modelling Heterogeneity in Survival Data,” Journal of Applied Probability, 28, 695–701.MathSciNetMATHCrossRefGoogle Scholar
- Kimber, A.C. and Crowder, M.J. (1990), “A Repeated Measures Model with Applications in Psychology,” British Journal of Mathematical and Statistical Psychology, 43, 283–292.CrossRefGoogle Scholar
- Takahasi, K. (1965), “Note on the Multivariate Burr’s Distribution,” Annals of the Institute of Statistical Mathematics, 17, 257–260.MathSciNetMATHCrossRefGoogle Scholar
- Vaupel, J.W., Manton, K.G. and Stallard, E. (1979), “The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality,” Demography, 16, 439–454.CrossRefGoogle Scholar
- Whitmore, G.A. and Lee, M-L.T. (1991), “A Multivariate Survival Distribution Generated by an Inverse Gaussian Mixture of Exponentials,” Technometrics, 33, 39–50.MathSciNetMATHCrossRefGoogle Scholar
Copyright information
© Springer Science+Business Media Dordrecht 1996