Which estimator is the product-limit estimator used to estimate the survivor function?

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The product-limit estimator is the Kaplan-Meier estimator of the survivor function. It builds the survival curve nonparametrically by multiplying the conditional survival probabilities at each observed event time. If at a time ti there are di events among ni individuals at risk just before ti, the probability of surviving past that time given survival to ti is (ni − di)/ni. Multiplying these conditional surpluses over all event times up to t gives Ŝ(t) = ∏_{ti ≤ t} (1 − di/ni). This yields a step-function estimate that properly handles right-censoring because censored individuals still contribute to the risk set up to their censoring time, influencing ni but not adding to di. The Kaplan-Meier estimator is distinct from the Nelson-Aalen estimator (which targets the cumulative hazard), actuarial life tables (discrete approximations), and the Cox model (hazard regression with covariates).