Generalized logistic frailty model. (English) Zbl 1251.90104
Summary: We propose a new reliability model which is a generalization of the logistic frailty model first considered by J. W. Vaupel [“Kindred lifetimes: frailty models in population genetics”, in: J. Adams, D. A. Lam, A. I. Hermalin and P. Smouse (eds.), Convergent issues in genetics and demography, Oxford: Oxford University Press, 155–170 (1991), http://user.demogr.mpg.de/jwv/pdf/Kindred_Lifetimes.pdf] for fitting human mortality data. Essentially, a shape parameter is added to the existing model providing more flexibility in modeling lifetime data. Several model properties such as the survival function, density and the hazard rate are investigated. In particular, we show that the model is very versatile; it is able to take a variety of non-monotonic hazard rate shapes. Parameters estimation is also considered. Two well-known survival data sets are satisfactorily fitted by the proposed distribution, and its goodness-of-fit is compared.
MSC:
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
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