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The Kaplan and Meier method, also known as the product-limit estimator, is a non-parametric technique used in survival analysis to estimate the survival function from lifetime data. It is particularly useful when the data are subject to censoring, which occurs when the exact survival time for some individuals is not known due to loss to follow-up, withdrawal, or the end of the study period. Unlike parametric methods, it does not assume any specific probability distribution for survival times, making it widely applicable in medical research, engineering reliability studies, and social sciences. Let T be a non-negative random variable representing survival time. The survival function S(t) is defined as the probability that an individual survives beyond time t, that is, S(t) = P(T > t). The Kaplan–Meier estimator calculates this survival function as a step function that changes value only at observed event times. Suppose there are _____ ___ ___ ______ ________ ___.
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