Description

This issue is a feature proposal.

Beta negative binomial distribution is three-parameter discrete distribution, often used to model overdispersed count data or data with a heavy tail.

PMF:

$$f(n|r, \alpha ,\beta)={\frac {\Gamma (r+n)}{n!\Gamma (r)}}{\frac {\Gamma (\alpha +r)\Gamma (\beta +n)\Gamma (\alpha +\beta )}{\Gamma (\alpha +r+\beta +n)\Gamma (\alpha )\Gamma (\beta )}}$$

where

$$n \in \mathbb {N} _{0}, \quad r > 0, \quad \alpha > 0, \quad \beta > 0$$

Tagging @s-mishra and @olli0601 to track the process.

Expected Output

real beta_neg_binomial_lpmf(ints n, reals r, reals alpha, reals beta)

Checklist

This will require a beta_neg_binomial_lpmf with analytical derivatives.

• _lpmf

Tests

• _lpmf

Current Version:

v4.9.0