In teachingApps: Apps for Teaching Statistics, R Programming, and Shiny App Development

Properties of the Survival Function

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• 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

teachingApps documentation built on July 1, 2020, 5:58 p.m.