Best way to fit data from one histogram into another?

Question

I'm predicting some data, and I have a fairly good idea what the end histogram should look like.

Here, the top is 'ground truth' (should be what the data should look like). The bottom is what I've currently predicted.

Are there any known techniques for trying to use histogram results as a way to better guide fitting / prediction?

Answer 1

The approach I used was using sklearn.linear_model.PoissonRegressor() which results in a normal distribution for my data. I'd like to try using hyperparameters for the PDF but not sure how to do that.