Let's say we have $k$ vectors each having $n$ counts, and we know that each of the those vectors are distributed by a Poisson distribution, but likely with very different means. I am wondering whether there is a way to normalize each of those $k$ vectors such that each of resulting $k$ vectors is distributed by a Poisson which has mean 1. That is, I am looking for something for Poisson which would correspond to subtracting the mean value from the Gaussian vectors with different means which would result in each vector being a 0-mean Gaussian.