Product-limit estimator is a method for estimating the survival functions for the set of survival times, some of which might be censored observations. The logic behind the procedure includes the product of a number of the conditional probabilities, so that, for instance, the probability of the patient surviving two days after a liver transplant can be measured as the probability of surviving one day, multiplied by the possibility of surviving the second day provided that the patient survived the first day. Particularly the estimator is given as follows