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

### Properties of The Hazard Function $h(t)$

• The cumulative hazard function relates the "accumulated" hazard rate over time

$$H(t)=\displaystyle \int_{0}^{t} h(t)dx$$

• The cumulative hazard function may also be used to compute the average hazard rate $T \in (t_1,t_2]$

\begin{aligned} AHR(t_1,t_2)&=\frac{\int_{t_{1}}^{t_{2}}h(u)du}{t_2-t_1}=\frac{H(t_2)-H(t_1)}{t_2-t_1}\\\\ AHR(0,t)&=\frac{\int_{0}^{t}h(u)du}{t}=\frac{H(t)}{t}\approx\frac{F(t)}{t}\;\;\text{ for }\; F(t) < 0.10 \end{aligned}

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