Exponential-rate estimation from censored exposure
= Exponential-rate estimation from censored exposure
{title2=$\widehat\lambda=d/X$}
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.