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Lifetime Modelling under Various Distributional Assumptions for Competing Risks

Iman Mabrouk, Serge B. Provost

Abstract



This article statistically compares several models in connection with systems exposed to two competing causes of failure. The models being considered are the generalized gamma, Weibull, gamma and exponential distributions as well as a certain extension of the inverse Gaussian distribution. The maximum likelihood approach is utilized to derive point estimates and asymptotic confidence intervals for the distributional parameters. Since the exponential, Weibull and gamma distributions are special cases of the generalized gamma distribution, log-likelihood ratio tests are used to determine whether the latter provides abetter fit than its particular cases when applied to an actual data set of failure times. In addition, Akaike’s information criterion is utilized to assess the goodness of fit of the generalized gamma distribution and the extension of the inverse Gaussian distribution. The relative risk rates associated with these distributions are also discussed. The results indicate that the extension of the inverse Gaussian distribution provides a superior fit as compared with the other distributions being considered for modelling a certain data set of failure times. Accordingly, the relative risk rates determined from the former should prove
more accurate.

Keywords


Competing risks models, generalized gamma distribution, modified inverse Gaussian distribution, maximum likelihood estimator, goodness of fit.

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