Systematic-error signal-to-noise ceiling
= Systematic-error signal-to-noise ceiling
{title2=$Z_\infty$}
Let $X\sim\operatorname{Poisson}(Q+B)$ and $Y\sim\operatorname{Poisson}(fB)$ be independent. Then $X-Y$ has source-estimation bias $(1-f)B$ and variance $Q+(1+f)B$. Its accuracy ratio $Q/\sqrt{\mathbb E[(X-Y-Q)^2]}$ tends to $R_Q/(|1-f|R_B)$ when $Q=R_QT$, $B=R_BT$ and $T$ grows. This uses <mean squared error>, not variance alone, and assumes a fixed uncorrected mismatch.