Closed-Form PMFs for PPCs

[ColtAllen]

While working on the upcoming BetaGeoBetaBinomModel, I found a closed-form solution in the research paper for the model's probability mass function (PMF). After doing some more digging I realized every CLV model has a closed-form expression.

Currently the distribution_new_customers method builds these PMFs from scratch via sampling. However, it should be more performant for PPCs (both prior and posterior) to use the closed-form PMF expressions.