= Poisson log-rate ratio
{c}
{title2=$\widehat\nu=\log\overline Y_B-\log\overline Y_A$}
For independent samples of $n$ observations from <Poisson distributions> with positive means $a$ and $b$, the <maximum-likelihood estimator> of $\nu=\log(b/a)$ is the displayed difference when both totals are positive. Its asymptotic variance is $(a^{-1}+b^{-1})/n$, obtained by the <delta method> or by inverting the two-parameter <Fisher information matrix>. A zero group total makes its log-mean estimate a boundary value; finite normal intervals require nonzero totals.
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