_def-hazard.qmd

:::{#def-hazard}

##### Hazard function, hazard rate, hazard rate function

::: notes
The **hazard function**, **hazard rate**,  **hazard rate function**, 
for a random variable $T$ at value $t$,
typically denoted as $h(t)$ or $\lambda(t)$,
is the conditional [density](probability.qmd#def-pdf) of $T$ at $t$, 
given $T \ge t$.
That is:
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$$\haz(t) \eqdef \p(T=t|T\ge t)$$

::: notes
If $T$ represents the time at which an event occurs, 
then $\haz(t)$ is the probability that the event occurs at time $t$, 
given that it has not occurred prior to time $t$.
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