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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 19:33, 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

H~(t)=titdini,

with di the number of events at ti and ni the total individuals at risk at ti.[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

  1. Template:Cite web
  2. Template:Cite web
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