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 In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the ...

is given by :

\tilde(t)=\sum_\frac,

with

d_i

the number of events at

t_i

and

n_i

the total individuals at risk at

t_i

. 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 process In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...

es. It was constructed by

Wayne Nelson Wayne Nelson (born June 1, 1950) is an American musician best known for being the current lead singer of the rock band Little River Band, in which he also plays bass. Shortly after his birth, Nelson's family moved to Rome, Illinois, a suburb ...

and Odd Aalen.

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{{DEFAULTSORT:Nelson-Aalen Estimator Life insurance Reliability engineering Survival analysis

See also

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Further reading

External links