Noise distribution in Pyro Forecasting Module


My problem: In the Pyro Forecasting Module, I have to specify a noise distribution. I understand its setup in the simple case where noise can be interpreted as an additive centered addon N(0, sigma) on the mean target prediction as in an ordinary linear regression setup. But how do I have to set it up when I model a target variable as, say by a Poisson or GammaPoisson distributed random variable? How do I have to set up the error/noise distribution in these cases?

Thanks for any help!