= Solution
The paper uses $F$ for the <survivor function>, rather than for the <cumulative distribution function>. For a nonnegative <survival time> $T$ with an absolutely continuous <probability distribution>, define
$$
F(t)=\Pr(T>t),\qquad f(t)=-F'(t).
$$
Where $F(t)>0$, the <hazard function> is the instantaneous event rate conditional on survival:
$$
h(t)=\lim_{\Delta\downarrow0}\frac{\Pr(t<T\leq t+\Delta\mid T>t)}{\Delta}
=\frac{f(t)}{F(t)}.
$$
The <integrated hazard> is $H(t)=\int_0^t h(u)\,du$. Since $h=-F'/F$, integration gives $H(t)=\log F(0)-\log F(t)$. With the usual time origin and no event at zero, $F(0)=1$, so
$$
\boxed{H(t)=-\log F(t),\qquad F(t)=e^{-H(t)},\qquad f(t)=h(t)e^{-H(t)}.}
$$
Conversely, differentiating $F=e^{-H}$ gives $F'=-hF$, so these relationships determine each of the <survivor function>, <hazard function> and <integrated hazard> from either of the others. A positive limiting <survivor function> is possible if the <integrated hazard> remains finite; a proper finite event time instead has $F(t)\to0$.
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