th/tex">h(t)</script> expresses the conditional probability that the event will occur within <script type="math/tex">[t, t+dt)</script> , given that it has not occurred before.
<script type="math/tex; mode=display">\begin{equation*}
h(t) = \lim_{dt \to 0} \frac{\text{Pr} \left[  t \leq T < t + dt\ | T \geq t\right ] }{dt} = \frac{f(t)}{S(t)} = -\frac{d}{dt}\log  S(t)
\end{equation*}</script>
</p>
<p>Thus, the hazard and Survival functions are linked by the following formula:
<script type="math/tex; mode=dis