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:

$$S(y)=1-F_Y(y)=P(Y\ge y).$$

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