 Solution

For administrative censoring with uniform entry, let entry time $A\sim \mathrm{Uniform}({\tau }_a,{\tau }_b)$. Then $C={\tau }_c-A$ has the uniform distribution on $[\ell ,r]$, where $\ell ={\tau }_c-{\tau }_b$, $r={\tau }_c-{\tau }_a$, and $d=r-\ell ={\tau }_b-{\tau }_a$. Its density and survivor function areDividing density by survival and integrating gives the censoring hazard and integrated hazard:The hazard function is undefined once no uncensored individuals remain. As $t\uparrow r$, it diverges like $1/(r-t)$ and the cumulative hazard function diverges logarithmically. This reflects the certainty of administrative censoring by the longest possible follow-up time, not dependence of censoring on the event process.