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Detection of frailty in Weibull lifetime data using outlier tests

Detection of frailty in Weibull lifetime data using outlier tests
Detection of frailty in Weibull lifetime data using outlier tests
Heterogeneity in lifetime data may be modelled by multiplying an individual's hazard by an unobserved frailty. We test for the presence of frailty of this kind in univariate and bivariate data with Weibull distributed lifetimes, using statistics based on the ordered Cox-Snell residuals from the null model of no frailty. The form of the statistics is suggested by outlier testing in the gamma distribution. We find through simulation that the sum of the k largest or k smallest order statistics, for suitably chosen k, provides a powerful test when the frailty distribution is assumed to be gamma or positive stable, respectively. We provide recommended values of k for sample sizes up to 100 and simple formulae for estimated critical values for tests at the 5% level.
weibull distribution, cox-snell residuals, testing
0094-9655
15-23
Caroni, C.
6fcc8200-11ae-496e-90ed-ed1fcf1ca147
Kimber, A.
40ba3a19-bbe3-47b6-9a8d-68ebf4cea774
Caroni, C.
6fcc8200-11ae-496e-90ed-ed1fcf1ca147
Kimber, A.
40ba3a19-bbe3-47b6-9a8d-68ebf4cea774

Caroni, C. and Kimber, A. (2004) Detection of frailty in Weibull lifetime data using outlier tests. Journal of Statistical Computation and Simulation, 74 (1), 15-23. (doi:10.1080/0094965031000104305).

Record type: Article

Abstract

Heterogeneity in lifetime data may be modelled by multiplying an individual's hazard by an unobserved frailty. We test for the presence of frailty of this kind in univariate and bivariate data with Weibull distributed lifetimes, using statistics based on the ordered Cox-Snell residuals from the null model of no frailty. The form of the statistics is suggested by outlier testing in the gamma distribution. We find through simulation that the sum of the k largest or k smallest order statistics, for suitably chosen k, provides a powerful test when the frailty distribution is assumed to be gamma or positive stable, respectively. We provide recommended values of k for sample sizes up to 100 and simple formulae for estimated critical values for tests at the 5% level.

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Published date: 2004
Keywords: weibull distribution, cox-snell residuals, testing
Organisations: Statistics

Identifiers

Local EPrints ID: 42005
URI: http://eprints.soton.ac.uk/id/eprint/42005
ISSN: 0094-9655
PURE UUID: 76939f6b-a02f-48b2-bf7b-484d5f1c959b

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Date deposited: 30 Oct 2006
Last modified: 13 Mar 2019 21:13

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