Let's say we have $k$ vectors each containing $n$ non-negative integers (counts), and we know that each of those vectors are distributed by a Poisson, each with a very different mean. I am wondering whether there is a way to normalize each of those $k$ vectors such that each of resulting $k$ vectors is approximately distributed by a Poisson with mean 1. That is, I am looking for a Poisson counterpart of subtracting the mean value from each of Gaussian vectors which result in each vector being a 0-mean Gaussian.
Solved – Normalizing (or standardizing) Poisson data
normalizationpoisson distributionstandardization
Best Answer
I don't think you can use a linear transform like you can with normally distributed RV's as the expectation and variance will not be equal which is forced under Poisson distributions (variance will be the constant multiple of your expectation).
The easiest way would just be to use the inverse CDF of your Poisson with mean = $\lambda$ then put this [0,1] through the CDF for a Poisson $\lambda$ = 1.