  We discuss nonparametric estimators of the distribution of the incubation
time of a disease. The classical approach in these models is to use parametric
families like Weibull, log-normal or gamma in the estimation procedure. We
analyze instead the nonparametric maximum likelihood estimator (MLE) and show
that, under some conditions, its rate of convergence is cube root $n$ and that
its limit behavior is given by Chernoff's distribution. We also study smooth
estimates, based on the MLE. The density estimates, based on the MLE, are
capable of catching finer or unexpected aspects of the density, in contrast
with the classical parametric methods. {\tt R} scripts are provided for the
nonparametric methods.
