In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse may be indicated by a relatively high number of individuals with large censored survival times. In this paper, the generalized log-gamma model is modifed for the possible presence of long-term survivors in the data. The models attempt to simultaneously estimate the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. The generalized log-gamma mixture model is exible enough to include many commonly used failure time distributions as special cases. We consider maximum likelihood and Jackknife estimators for the parameters of the model. 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