5 (source code)

= 5
{scope}

For a continuous proper event time with <cumulative hazard function> $H$ and <survivor function> $F(t)=e^{-H(t)}$, use the assumed inverse of $H$. For $u\ge0$,
$$
\mathbb P(H(T)>u)=\mathbb P(T>H^{-1}(u))=F(H^{-1}(u))=e^{-u}.
$$
Therefore \b[the integrated-hazard transformation is unit exponential]:
$$
\boxed{H(T)\sim\operatorname{Exp}(1).}
$$
This <cumulative hazard probability transformation> is the basis for the following survival-model residual diagnostics.