A score test for the multivariate Burr and other Weibull mixture distributions

Scandinavian Journal of Statistics

Volumn 24, Issue 3, 1997, Pages 419-432

  Crowder, Martin ^a   Kimber, Alan ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

Censored data; Failure times; Frailty; Mixture distributions; Multivariate Burr distribution; Random effects; Repeated measures; Survival data; Weibull distribution

Indexed keywords

EID: 0031476861     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00073     Document Type: Article

References (30)

1. Abramowitz, M. & Stegun, I. A. (1965). Handbook of mathematical functions. Dover, New York.
2. Al-Hussaini, E. K., Mousa, M. A. M. A. & Jaheen, Z. F. (1992). Estimation under the Burr type XII failure model based on censored data: a comparative study. Test 1, 47-60.
3. Burr, I. W. (1942). Cumulative frequency functions. Ann. Math. Statist. 13, 215-232.
4. Chesher, A. (1984). Testing for neglected heterogeneity. Econometrica 52, 865-872.
5. 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.
6. Crowder, M. J. (1985). A distributional model for repeated failure time measurements. J. Roy. Statist. Soc. Ser. B 47, 447-452.
7. Crowder, M. J. (1989). A multivariate distribution with Weibull connections. J. Roy. Statist. Soc. Ser. B 51, 93-107.
8. Crowder, M. J., Kimber, A. C., Smith, R. L. & Sweeting, T. J. (1991). The statistical analysis of reliability data. Chapman & Hall, London.
9. Durling, F. C. (1974). The bivariate Burr distribution. In Statistical distributions in scientific work, 1 (ed. by G. P. Patil et al.) 329-335, Pennsylvania State University Press, University Park, PA.
10. Everitt, B. S. & Hand, D. J. (1981). Finite mixture distributions. Chapman & Hall, London.
11. Feller, W. (1971). An introduction to probability and its applications, Vol. 2, 2nd ed. Wiley, New York.
12. Hougaard, P. (1984). Life table methods for heterogeneous populations: distributions describing the heterogeneity. Biometrika 71, 75-83.
13. Hougaard, P. (1986a). Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387-396.
14. Hougaard, P. (1986b). A class of multivariate failure time distributions. Biometrika 73, 671-678.
15. Hougaard, P. (1987). Modelling multivariate survival. Scand. J. Statist. 14, 291-304.
16. Hougaard, P. (1991). Modelling heterogeneity in survival data. J. Appl. Probab. 28, 695-701.
17. Hutchinson, T. P. (1981). Compound gamma bivariate distributions. Metrika 28, 263-271.
18. Kimber, A. C. & Crowder, M. J. (1990). A repeated measures model with applications in psychology. Br. J. Math. Statist. Psychol. 43, 283-292.
19. Lancaster, T. & Nickell, S. J. (1980). The analysis of re-employment probabilities for the unemployed (with discussion). J. Roy. Statist. Soc. Ser. A 143, 141-165.
20. Moore, R. J. (1982). Algorithm AS187: Derivatives of the incomplete gamma integral. Appl. Statist. 31, 330-335.
21. NAG (1988). Library Manual Mark 13. Numerical Algorithms Group, Oxford.
22. Nigm, A. M. (1988). Prediction bounds for the Burr model. Commun. Statist. - Theory Methods 17, 287-297.
23. Pearson, K. (1922). Tables of the incomplete gamma function. Cambridge University Press, London.
24. Pierce, D. A. (1982). The asymptotic effect of substituting estimators for parameters in certain types of statistics. Ann. Statist. 10, 475-478.
25. Self, S. G. & Liang, K-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610.
26. Takahasi, K. (1965). Note on the multivariate Burr's distribution. Ann. Inst. Statist. Math. 17, 257-260.
27. Tsai, H-T. (1990). Probabilistic tolerance design for a subsystem under Burr distribution using Taguchi's loss functions. Commun. Statist. - Theory Methods 19, 4679-4696.
28. Vaupel, J. W., Manton, K. G. & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16, 439-454.
29. Wall, H. S. (1948). Analytical theory of continued fractions. Van Nostrand, New York.
30. Whitmore, G. A. & Lee, M-L.T. (1991). A multivariate survival distribution generated by an inverse Gaussian mixture of exponentials. Technometrics 33, 39-50.