Comparison of the cumulative-hazard and Kaplan-Meier estimators of the survivor function

When both the product-limit (Kaplan-Meier) and the cumulative-hazard estimates of the Sf are calculated for the same data set, the survival probabilities obtained using the cumulative hazard approach are generally slightly larger than the ones obtained using the product-limit (Kaplan-Meier) approach. This heuristic inter-relation can not be specific to particular data sets; thus this paper shows that it holds consistently. More specifically, this paper proves this empirical relation of a regular deviation between the two main nonparametric reliability estimators