# Cutoff for a poisson-gaussian mixture model

I have count data that is bounded on one side at zero (see image). It is bimodal and I think it results from two different processes. I would like to fit a poisson distribution around the hump around zero, and a gaussian distribution around the hump at higher values. Then, I would like to find a cutoff separating the values into the two distributions. However, I'm struggling to find a method in R to do so. Does anyone know of an R package that can do this?

• This would be a truly strange thing to do because the Poisson distribution is supported only on the natural numbers but the Gaussian is a continuous distribution supported everywhere. I'm sure there won't be any R package to do this! BTW, one can eyeball this plot and see that any Poisson-shaped component could account only for some of the values between $0$ and $4,$ making it obvious a Gaussian wouldn't even be a bad approximation to the rest. Rather than pursuing this dead end, why don't you tell us what your underlying problem is? – whuber Dec 18 '20 at 22:11
• Thanks whuber, that's really informative. My problem: I start off with single cell RNAseq data (a matrix of cols = cells, rows = genes, values = UMI counts). My data is the number of cells a gene is not expressed in (the no. of 0s in each row). scRNAseq data is zero inflated. I expect a subset of 0 values to be artefacts. My goal is to identify those genes which possess mostly 'true' 0s vs artifactual 0s. My hunch is that the R hump represents those genes dominated by artifactual 0s and the L hump predominantly 'true' 0s. I aim to find the cutoff that separates these 2 distributions. – jmah Dec 18 '20 at 22:50