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| The '''survival function''', also known as a '''survivor function''' or '''reliability function''', is a property of any [[random variable]] that maps a set of events, usually associated with mortality or failure of some system, onto [[time]]. It captures the [[probability]] that the system will [[survival analysis|survive]] beyond a specified time.
| | 42 yr old Wine Maker Woodrow Paster from Thornbury, likes bmx, health and fitness and compose music. Advocates that you just visit Mount Athos.<br><br>My web page: [http://stemlessonplans.com/blog/view/55426/major-depression-and-steroids-hazards-for-body-weight-lifters Best Body Nutrition Weight Gainer] |
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| The term ''reliability function'' is common in [[engineering]] while the term ''survival function'' is used in a broader range of applications, including human mortality. Another name for the survival function is the '''complementary cumulative distribution function'''.
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| ==Definition==
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| Let ''T'' be a continuous random variable with [[cumulative distribution function]] ''F''(''t'') on the interval <nowiki>[0,∞)</nowiki>. Its ''survival function'' or ''reliability function'' is:
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| :<math>R(t) = P(\{T > t\}) = \int_t^{\infty} f(u)\,du = 1-F(t).</math> | |
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| ==Properties==
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| Every survival function ''R''(''t'') is [[monotonic function|monotonically decreasing]], i.e. <math>R(u) \le R(t)</math> for all <math>u > t</math>.
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| The [[time]], ''t'' = 0, represents some origin, typically the beginning of a study or the start of operation of some system. ''R''(0) is commonly unity but can be less to represent the [[probability]] that the system fails immediately upon operation.
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| The survivor function is left-continuous.
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| ==See also==
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| {{Portal|Statistics}}
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| *[[Survivorship curve]]
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| *[[Survival analysis]]
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| *[[Failure rate]]
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| *[[Mean time to failure]]
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| *[[Kaplan–Meier estimator]]
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| {{Statistics|analysis}}
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| {{DEFAULTSORT:Survival Function}}
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| [[Category:Survival analysis]]
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| [[Category:Probability theory]]
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| {{probability-stub}}
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| [[de:Überlebensfunktion]]
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| [[fr:Analyse de survie#Fonction de survie]]
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42 yr old Wine Maker Woodrow Paster from Thornbury, likes bmx, health and fitness and compose music. Advocates that you just visit Mount Athos.
My web page: Best Body Nutrition Weight Gainer