I was checking the radfit {vegan} package in R, and here is what they have for the Log-normal rank abundance distribution:

Function rad.lognormal fits a log-Normal model which assumes that the logarithmic abundances are distributed Normally, or a[r] = exp(log(mu) + log(sigma) * N), where N is a Normal deviate.

a[r] is the abundance of species at the rank of r. I think they've missed the variable "r" in their equation, right?

Here is the equation for Zipf for example: Function rad.zipf fits the Zipf model a[r] = Jp1r^gamma where p1 is the fitted proportion of the most abundant species, and gamma is a decay coefficient.

Any idea? Thanks!