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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

<math>\tilde{H}(t)=\sum_{t_i\leq t}\frac{d_i}{n_i},</math>

with <math>d_i</math> the number of events at <math>t_i</math> and <math>n_i</math> the total individuals at risk at <math>t_i</math>.[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]

See also

References

  1. ^ "Kaplan–Meier and Nelson–Aalen Estimators". 
  2. ^ "Kaplan–Meier Survival Estimates". 
  3. ^ 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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