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.

exponential distribution (http://planetmath.org/ExponentialRandomVariable), with $S(y)=\exp(-\gamma y).$
2.

Weibull distribution, with $S(y)=\exp(-y^{\gamma})$ using the standard Weibull distribution.
3.

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