Exponential-rate estimation from censored exposure ($\hat{\lambda }=d/X$)

Under independent censoring and a constant event rate, $d$ observed events over total observed person-time $X$ give likelihood proportional to ${\lambda }^d{e}^{-\lambda X}$ and estimate $d/X$ for $d,X>0$. Censored observations belong in $X$. With no events the positive-rate likelihood has a boundary supremum.