Interval Estimation for the Parameters of the Modified Weibull Distribution Model with Censored Data: a Simulation Study

G.C. Perdoná, F. Louzada Neto

Abstract


Expressing the lifetime behavior through its hazard enables us to derive special classes of failure distributions according to the hazard pattern. The usual lifetime distributions, as both exponential and Weibull models, accommodate constant (exponential) and increasing/decreasing (Weibull) hazard functions. Nevertheless, in practice, it is common to find lifetime data with hazard function of different types, for example, a U-shaped hazard function. In the present paper we investigate the properties of the modified Weibull model [8], a three-parameter model which allows U-shaped hazards to be accommodated. Inferences for this model’s parameters based on both complete and censored samples are presented. We discuss different parametrizations as well as the interval estimation for the parameters of this model.

References


[1] M.V. Aarset, How to identify bathtub hazard rate, IEEE Transactions on Reliability, 36, No. 1 (1987), 106-108.

J.O. Berger, D. Sun, Bayesian analysis for the poly-Weibull distribution, Journal of the American Statistical Association, 88 (1993), 1412–1417.

Biggar et al., Perinatal intervention trial in Africa: effect of a birth canal cleansing intervention to prevent HIV transmission. Lancet 15, 347 (1996), 1647-50.

D.R. Cox, D.V. Hinkley, “Theoretical Statistics”, Chapman and Hall, London, 1974.

A.C. Davison, D.V. Hinkley, “BootstrapMethods and their Application”, Cambridge University Press, Cambridge, 1997.

N. Ebrahimi, The effect of misclassification of the actual cause of death in competing risks analysis, Statistics in Medicine, 15 (1996), 1557–1566.

W.W. Hauck, L.J. McKee, B.J. Turner, Two-part survival models applied to administrative data for determiningrate of and predictors for maternal–child transmission of HIV, Statistics in Medicine, 16 (1997), 1683– 1694.

C.D. Lai, M. Xie, N.P. Murthy, A modified Weibull distribution, IEEE Transactions on Reliability, 52 (2003), 33-37.

J.F. Lawless, “Statistical Models and Methods for Lifetime Data”, John Wiley, New York, 1982.

F. Louzada-Neto, Polyhazard regression models for lifetime data, Biometrics, 55 (1999), 1281-1285.

G.S. Mudholkar, D.K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42 (1993), 99-302.

G.S. Mudholkar, D.K. Srivastava, G.D. Kollia, A generalization of the Weibull distribution with application to the analysis of survival data, Journal of the American Statistical Association, 91, No. 436 (1996), 1575-1583.

A.N.F. Silva, “Estudo Evolutivo das Criançaas Expostas ao HIV e Notificadas pelo Núcleo de Vigilância Epidemiológica do HCFMRP-USP”, M.Sc. Thesis, University of São Paulo, Brazil, 2004.




DOI: https://doi.org/10.5540/tema.2008.09.03.0437

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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