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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 $u\ge 0$,Therefore the integrated-hazard transformation is unit exponential:This cumulative hazard probability transformation is the basis for the following survival-model residual diagnostics.

Throughout the survival questions, use the paper's notation $F(t)=\mathbb{P}(T>t)$ for the survivor function, not for a cumulative distribution function. To construct the Kaplan–Meier estimator, sort the distinct observed event times $a_j$. Let $r_j$ be the size of the risk set immediately before $a_j$, and $d_j$ the number of events at that time. The estimated conditional chance of surviving that event time is $1-d_j/r_j$. Multiplying these conditional probabilities givesA right censoring time reduces later risk sets but causes no jump itself. The usual interpretation as a population survivor function uses independent censoring.