Nelson–Aalen estimator

The Nelson–Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. It is used in survival theory, reliability engineering and life insurance to estimate the cumulative number of expected events. An "event" can be the failure of a non-repairable component, the death of a human being, or any occurrence for which the experimental unit remains in the "failed" state (e.g., death) from the point at which it changed on. The estimator is given by

with ${\displaystyle d_{i}}$ the number of events at ${\displaystyle t_{i}}$ and ${\displaystyle n_{i}}$ the total individuals at risk at ${\displaystyle t_{i}}$.

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