Survival Function
Definition
The survival function (or reliability function) of a random variable $X$ is
$$ S(x) = \mathbb{P}(X > x) = 1 - F(x), $$where $F(x)$ is the cumulative distribution function.
Properties
- $S(x)$ is non-increasing.
- $S(-\infty) = 1$ and $S(\infty) = 0$.
- For a continuous random variable with PDF $f$: $S(x) = \int_x^{\infty} f(t)\, dt$.