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{{More footnotes|date=November 2010}}
The '''Nelson–Aalen estimator''' is a [[non-parametric statistics|non-parametric estimator]] of the cumulative [[hazard rate]] function in case of [[Censoring (statistics)|censored data]] or [[missing data|incomplete data]].<ref>{{cite web |url=http://tkchen.wordpress.com/2008/09/21/kaplan-meier-and-nelson-aalen-estimators/|title=Kaplan-Meier and Nelson-Aalen Estimators}}</ref> It is used in [[survival analysis|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>


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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>.<ref>{{cite web |url=http://www.statsdirect.com/help/survival_analysis/kaplan.htm|title=Kaplan-Meier Survival Estimates}}</ref>
 
The curvature of the Nelson–Aalen estimator gives an idea of the hazard rate shape. A concave shape is an indicator for [[bathtub curve|infant mortality]] while a convex shape indicates [[bathtub curve|wear out mortality]].
 
It can be used for example when testing the homogenitity of [[Poisson process]]es.<ref>{{cite journal |first=Jan |last=Kysely |first2=Jan |last2=Picek |first3=Romana |last3=Beranova |year=2010 |title=Estimating extremes in climate change simulations using the peaks-over-threshold method with a non-stationary threshold |journal=Global and Planetary Change |volume=72 |issue=1-2 |pages=55–68 |doi=10.1016/j.gloplacha.2010.03.006 }}</ref>
 
==See also==
* [[Kaplan–Meier estimator]]
 
==References==
{{Reflist}}
 
==External links==
 
{{DEFAULTSORT:Nelson-Aalen Estimator}}
[[Category:Life insurance]]
[[Category:Reliability engineering]]
[[Category:Survival analysis]]

Revision as of 20:33, 6 January 2014

Template:More footnotes 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

with the number of events at and the total individuals at risk at .[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 homogenitity of Poisson processes.[3]

See also

References

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External links

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  2. Template:Cite web
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