A procedure for estimating the survivor function (see hazard rate) from observations of lifetimes (of people, machine components, etc.) when some observations are censored (e.g. people move away from the observation site, or functioning components are removed before the end of the experimental period). The estimate is calculated as follows. First, order the data by length of lifetime. Suppose there are m distinct lifetimes (where, for example, people alive at the time of calculation are given their current lifetime). Let t_(j) be the jth of these ordered lifetimes, let n_j individuals have lifetimes of t_(j) or more, and let d_j individuals have lifetimes of exactly t_(j). The Kaplan–Meier estimate of the survivor function is given byThe corresponding estimator has variance estimated by the Greenwood formulaClosely related to the Kaplan–Meier estimate is the Nelson–Aalen estimate of the cumulative hazard rate, given by

http://www.ms.uky.edu/~mai/java/stat/KapMei.html Applet.