Abstract
The Weibull distribution is a natural starting point in the modelling of failure times in reliability, material strength data and many other applications that involve lifetime data. In recent years there has been a growing interest in modelling 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 yields a tractable and flexible generalization of the Weibull distribution. In this note a score test for detecting heterogeneity in this context is discussed and illustrated using some infant nutrition data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
American Academy of Pediatrics, Committee on Nutrition, “On the feeding of supplemental foods to infants,” Pediatr. vol. 65 pp. 1178–1181, 1980.
D. Commenges and P. K. Andersen, “Score test of homogeneity for survival data,” Lifetime Data Analysis vol. 1 pp. 145–156, 1995.
M. J. Crowder, “A distributional model for repeated failure time measurements,” J. Roy. Statist. Soc. vol. B47 pp. 447–452, 1985.
M. J. Crowder, “A multivariate distribution with Weibull connections,” J. Roy. Statist. Soc. vol. B51 pp. 93–107, 1989.
M. J. Crowder and A. C. Kimber, “A score test for the multivariate Burr and other Weibull mixture distributions,” To appear, 1995.
M. J. Crowder, A. C. Kimber, R. L. Smith and T. J. Sweeting, Statistical Analysis of Reliability Data. Chapman and Hall: London, 1991.
European Society of Paediatric Gastroenterology and Nutrition, Committee on Nutrition, “Guidelines on infant nutrition: recommendations for infant feeding,” Acta Paediatr. Scand., suppl. 302, 1982.
R. J. Gray “Tests for variation over groups in survival data,” J. Amer. Statist. Ass. vol. 90 pp 198–203, 1995.
P. Hougaard, “Life table methods for heterogeneous populations: distributions describing the heterogeneity,” Biometrika vol. 71 pp. 75–83, 1984.
P. Hougaard, “Survival models for heterogeneous populations derived from stable distributions,” Biometrika vol. 73 pp. 387–396, 1986a.
P. Hougaard, “A class of multivariate failure time distributions,” Biometrika vol. 73 pp. 671–678, 1986b.
P. Hougaard, “Modelling multivariate survival,” Scand. J. Statist. vol. 14 pp. 291–304, 1987.
P. Hougaard, “Modelling heterogeneity in survival data,” J. Appl. Probab. vol. 28 pp. 695–701, 1991.
A. C. Kimber and M. J. Crowder, “A repeated measures model with applications in psychology,” Br. J. Math. Statist. Psychol. vol. 43 pp. 283–292, 1990.
K-Y. Liang, “A locally most powerful test for homogeneity with many strata,” Biometrika vol. 74 pp. 259–264, 1987.
R. J. Moore, “Derivatives of the incomplete gamma integral,” Appl. Statist. vol. 31 pp. 330–333, 1982.
D. A. Pierce, “The asymptotic effect of substituting estimators for parameters in certain types of statistics,” Ann. Statist. vol. 10 pp. 475–478, 1982.
J. H. Shih and T. A. Louis, “Assessing gamma frailty models for clustered failure time data,” Lifetime Data Analysis vol. 1 pp. 205–220, 1995.
S. A. M. van den Boom, “Feeding practices and growth of children under 20 months of age in Madrid,” University of Surrey PhD Thesis, 1994.
S. A. M. van den Boom, A. C. Kimber and J. B. Morgan, “Type of milk feeding in infants and young children up to 19 months of age in three socio-economic groups in Madrid,” Acta Paediatr. vol. 82 pp. 1017–1023, 1992.
S. A. M. van den Boom, A. C. Kimber and J. B. Morgan, “Weaning practices of children up to 19 months in Madrid,” To appear, 1995.
J. T. Wassell, G. W. Kulczycki and E. S. Moyer, “Frailty models of manufacturing effects,” Lifetime Data Analysis vol. 1 pp. 161–170, 1995.
G. A. Whitmore and M-L. T Lee, “A multivariate survival distribution generated by an inverse Gaussian mixture of exponentials,” Technometrics vol. 33 pp. 39–50, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kimber, A.C. A Weibull-based score test for heterogeneity. Lifetime Data Anal 2, 63–71 (1996). https://doi.org/10.1007/BF00128471
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00128471