In this paper the generalized log-gamma model is modi ed for possibility that
long-term survivors may be present in the data. The model attempts to separately
estimate the effects of covariates on the acceleration/deceleration of the
timing of a given event and 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. We consider maximum likelihood and
Jackknife estimators for the parameters of the model. We derive the appropriate
matrices for assessing local in uence on the parameter estimates under di erent
perturbation schemes and we also present some ways to perform global in uence.
Finally, a data set from the medical area is analyzed under the log-gamma generalized
mixture model. A residual analysis is performed in order to select an
appropriate model.