Derive equations/techniques for a mixture of Double Poissons

[spencermyoung513]

One method we want to experiment with in our paper is training an ensemble of neural networks with the Double Poisson NLL loss and combining their outputs with some mixture model (this paper presents a technique for doing this with an ensemble of networks trained with Gaussian NLL). We need:

• [x] A theoretical definition of a mixture of Double Poissons (preferably with closed-form equations for the parameters of the final distribution)
• [x] An implementation of the mixture model, with results on benchmark

[spencermyoung513]

Notebook with interesting mixture results / implementation here: https://github.com/porterjenkins/deep_uncertainty/blob/exp/mixture-of-dpo/deep_uncertainty/notebooks/double_poisson_mixture.ipynb