VST for negative binomial random variable https://en.wikipedia.org/wiki/Variance-stabilizing_transformation
The variance stabilizing transform of a Poisson random variable is the Anscombe transform. What is the VST for a negative binomial random variable?

Take a look at Anscombe's paper from 1948 the transformation of Poisson, Binomial and Negative-Binomial data. There, he shows that for a random variable
$$
Y \sim \text{NegBin}(m, k),
$$
where $m$ is the mean and $k$ is the size, the transformation
$$
Z = \sinh^{-1}\sqrt{\frac{Y + c}{k - 2c}}
$$
with $c \approx 3/8$ is in some sense optimal.
