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Survival models for heterogeneous populations derived from stable distributions
Abstract
A new three-parameter family of distributions on the positive numbers is proposed. It includes the stable distributions on the positive numbers, the gamma, the degenerate and the inverse Gaussian distributions. The family is characterized by the Laplace transform, from which moments, convolutions, infinite divisibility, unimodality and other properties are derived. The density is complicated, but a simple saddlepoint approximation is provided. Weibull and Gompertz distributions are naturally mixed over some of the distributions. The family is natural exponential in one of the parameters. The distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations. Desirable properties of such distributions are discussed. As an example survival after myocardial infarction is considered.
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Citations
Cited by
Statistical Inference Procedures for Bivariate Archimedean Copulas
Genest, C., & Rivest, L.-P. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476372 · Cited by 1,251
Regression with Frailty in Survival Analysis
McGilchrist, C. A., & Aisbett, C. W. (1991) · Biometrics · doi:10.2307/2532138 · Cited by 526
Frailty Models in Survival Analysis
Wienke, A. (2010) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420073911 · Cited by 454
Fluctuations of Lévy Processes with Applications: Introductory Lectures
Kyprianou, A. E. (2014) · Universitext · doi:10.1007/978-3-642-37632-0 · Cited by 373
Heterogeneity in survival analysis
Aalen, O. O. (1988) · Statistics in Medicine · doi:10.1002/sim.4780071105 · Cited by 366
Metadata
- Authors
- HOUGAARD, P.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1986
- Volume
- 73
- Issue
- 2
- Pages
- 387-396
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2076610368
- Cited by
- 716
- References
- 0
- FWCI
- 7.97
- Type
- journal article
- Language
- en
- Open access
- closed
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- HOUGAARD, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika. https://doi.org/10.1093/biomet/73.2.387
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