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Survival Function

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore related to a continuous probability density function P(x) by

S(x)=P(X>x)=int_x^(x_(max))P(x^')dx^',
(1)

so P(x). Similarly, the survival function is related to a discrete probability P(x) by

S(x)=P(X>x)=sum_(X>x)P(x).
(2)

The survival function S(x) and distribution function D(x) are related by

D(x)+S(x)=P(X<=x)+P(X>x)=1,
(3)

since probability functions are normalized.

See also

Distribution Function

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References

Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, p. 13, 2000.

Referenced on Wolfram|Alpha

Survival Function

Cite this as:

Weisstein, Eric W. "Survival Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SurvivalFunction.html

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