Normalizing (or standardizing) Poisson data 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.
 A: The variance stabilizing transformation of the Poisson distribution is to take the square root. Once you have done that, the variance is approximately 1/4. So to change to a variance of 1 you would just need to $2\cdot\sqrt{\lambda_k}$ for each of your $k$ vectors. 
This still does not make the means the same though for each of your vectors. To do that you would still need to subtract the mean of the transformed data. 
Also see the Wikipedia page on the Anscombe transform for additional options with Poisson data. Note all of these transforms frequently recommend the mean of the series be about 5, under that and they just have too few of values and will never look symmetric. That is a limitation, even with the CDF transform recommended by Tilefish.
I have not seen any simple transforms recommended for negative binomial distributions, so the CDF approach may be the best option. In this article though I do some simulations and show that simply adding 1 sigma (for control charting) after the $2\cdot\sqrt{\lambda_k}$ transform produces pretty close to nominal coverage. 
A: 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.
