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
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended functi ...
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
the number of events at time
and
the total individuals at risk at
.
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.
It was constructed by
Wayne Nelson and
Odd Aalen.
The Nelson-Aalen estimator is directly related to the
Kaplan-Meier estimator and both maximize the
empirical likelihood.
[Zhou, M. (2015). Empirical Likelihood Method in Survival Analysis (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b18598, https://books.google.com/books?id=9-b5CQAAQBAJ&dq=Does+the+Nelson%E2%80%93Aalen+estimator+construct+an+empirical+likelihood%3F&pg=PA7]
References
Further reading
*
External links
{{DEFAULTSORT:Nelson-Aalen Estimator
Life insurance
Reliability engineering
Survival analysis