Lecture 10: Kaplan–Meier estimator (product-limit estimator) for F

Now we can introduce the desired estimator for the distribution function F of lifetimes, based on censored observations.

Since Mn accumulates the “purely noisy” component of Nn, we obtain our estimator by equating Mn to zero, that is, as a solution to the equation

dF(y) 1−F(y) = 0, 0≤ t ≤ T˜(n), (10.1)

with respect to F . Here T˜(n) is the moment of the last jump of the process Yn.