---
output: html_document
---

# Properties of the Survival Function

<hr/>

- The survival function relates the probability that the true (but unknown) value of $T$ is greater than $t$ 

$$S(t)=Pr(T > t), t\in (0,\infty)$$

- The survival function is strictly positive 

$$S(t) \ge 0, \forall t \in \mathbb{R}^{+}$$

- The survival function is non-increasing 

$$\begin{aligned}S(0)&=1\\\\\\\\
\displaystyle\lim_{t \to \infty} S(t)&=0\end{aligned}$$

- Alternate names

    + The reliability function
    
    + The complementary cumulative distribution function
