Definition

Let $T_{i}, i = 1, 2, \dots, n$ be i.i.d. random variables with the Survival Function $S (t)$ , then the empirical survival function is defined as $\hat{S} (t) = \frac{1}{n} i = 1 \sum n I (T_{i} > t)$ Since $I (T_{i} > t)$ is a Bernoulli trial, $n \hat{S} (t) \sim B (n, S (t))$