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