  In survey analysis, the estimation of the cumulative distribution function
(cdf) is of great interest: it allows for instance to derive quantiles
estimators or other non linear parameters derived from the cdf. We consider the
case where the response variable is a right censored duration variable. In this
framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As
an alternative, we propose a nonparametric model-based estimator of the cdf in
a finite population. The new estimator uses auxiliary information brought by a
continuous covariate and is based on nonparametric median regression adapted to
the censored case. The bias and variance of the prediction error of the
estimator are estimated by a bootstrap procedure adapted to censoring. The new
estimator is compared by model-based simulations to the Kaplan-Meier estimator
computed with the sampled individuals: a significant gain in precision is
brought by the new method whatever the size of the sample and the censoring
rate. Welfare duration data are used to illustrate the new methodology.
