We often assume that an abundance estimate is log-normally distributed and use that as a basis for constructing confidence intervals. This is an *aide memoire* for me on that topic…

We’ve estimated the abundance of some population using some method^{1} and now have an estimated abundance, which we’ll call $\hat{N}$ and an associated estimate of the variance $\widehat{\text{Var}}(\hat{N})$.

So we assume:
for R’s sake (for things like `qlnorm`

and `plnorm`

etc) we need the following parameters:

So if we know^{2} that:
and
we can get back to expressions about $\mu$ and $\sigma$. For $\sigma$ first…
and for $\mu$:

These values can then be fed to `qlnorm`

to obtain confidence intervals, hurrah!