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.^[1] 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

{\tilde {H}}(t)=\sum _{{t_{i}\leq t}}{\frac {d_{i}}{n_{i}}},

with $d_{i}$ the number of events at $t_{i}$ and $n_{i}$ the total individuals at risk at $t_{i}$ .^[2]

The curvature of the Nelson–Aalen estimator gives an idea of the hazard rate shape. A concave shape is an indicator for infant mortality while a convex shape indicates wear out mortality.

It can be used for example when testing the homogeneity of Poisson processes.^[3]

References

↑ "Kaplan–Meier and Nelson–Aalen Estimators".
↑ "Kaplan–Meier Survival Estimates".
↑ Kysely, Jan; Picek, Jan; Beranova, Romana (2010). "Estimating extremes in climate change simulations using the peaks-over-threshold method with a non-stationary threshold". Global and Planetary Change. 72 (1-2): 55–68. doi:10.1016/j.gloplacha.2010.03.006.

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Nelson–Aalen estimator

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References

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