In this task X ~ NB(r, p), where X is the random variable (the observed number of comments on a blog post from a given blog) and NB refers to the negative binomial distribution. Additionally, I’ve taken a Bayesian view of r and p for the parameters of the negative binomial, choosing to view them as random variables as well. I’ve modeled r using a beta prime and p as a beta. Computing the exact Bayesian distribution for X was overkill for my use case and not terribly computationally efficient, so I chose to use maximum-a-posteriori estimates for r and p when computing the distribution of X for a blog.

I hope this helps clarify how I’ve modeled blog post comment counts.

I apologize for two typos, i.e., Y=X/(1+X) (should be Y=X/(1-X)) and X=Y/(1-Y) (should be X=Y/(1+Y)) in my earlier comment.

As mentioned, “if X ~ Beta(a, b), then Y = X/(1+X) ~ Beta’(a, b)”. In another word, if Y ~ Beta’(a, b), then X = Y/(1-Y) ~ Beta(a, b). If `Y’ is substituted by r, which variable will be the substitution of `X’?