Survival Function

Definition

Survival Function $S(t)$: $S(t)=\mathrm{Pr}(T>t)$

The probability of surviving beyond time $t$.

Properties

• Monotonically decreasing
• $S(0)=1$ (starts at 1)
• $\lim \_t\to \infty S(t)=0$ (approaches 0)

Relationships

$S(t)=1-F(t)=\exp \text{[}-H(t)]$

where:

• $F(t)$ = cumulative distribution function
• $H(t)$ =cumulative hazard function

Related

• Hazard Function
• Cumulative Hazard