= Discrete hazard
{title2=$h_j=\mathbb P(T=t_j\mid T>t_{j-1})$}
At ordered possible failure times $t_j$, the <discrete hazard> is $h_j=\mathbb P(T=t_j\mid T>t_{j-1})$. Its <survival function> satisfies $S(t_j)=S(t_{j-1})(1-h_j)$, and hence $S(t)=\prod_{t_j\le t}(1-h_j)$. Estimating $h_j$ by the observed number of failures divided by the <risk set> size under <independent censoring> yields the <Kaplan–Meier estimator>. Unlike a continuous-time hazard rate, a <discrete hazard> is a probability between zero and one.
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