# survivor function

Let $Y$ be a random variable with cumulative probability distribution function $F_{Y}(y)$. Then the survivor function $S(y)$ is defined to be:

 $S(y)=1-F_{Y}(y)=P(Y\geq y).$

The random variable $Y$ is often called the survival time.

The survivor function is the probability of survival beyond time $Y=y$.

Examples. The three most commonly used distribution functions for survival time are:

1. 1.

exponential distribution (http://planetmath.org/ExponentialRandomVariable), with $S(y)=\exp(-\gamma y).$

2. 2.

Weibull distribution, with $S(y)=\exp(-y^{\gamma})$ using the standard Weibull distribution.

3. 3.

extreme-value distribution, with $S(y)=\exp(-\exp(\displaystyle{\frac{y-\alpha}{\beta}})).$

Title survivor function SurvivorFunction 2013-03-22 14:27:43 2013-03-22 14:27:43 CWoo (3771) CWoo (3771) 6 CWoo (3771) Definition msc 62N99 msc 62P05 survival time