Since the publication of their truncated smooth estimator of a survival function in 1996, Chaubey and Sen continued investigation into its statistical properties under various conditions. The authors had identified a problem of convergence of their estimator when estimating the mean residual life function. To overcome this problem with the convergence, they proposed an untruncated version of their smooth estimator. Nevertheless, in fear of oversmoothing with the untruncated version, the authors did not pursue research on this estimator much further.  This thesis deals with the investigation of some statistical properties of the untruncated version of the smooth estimator and studies the problem of oversmoothing by using simulations.