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add Bell distribution
This feature request would add support for the Bell distribution. The Bell distribution is suitable for count data, has a single parameter, and can model overdispersed counts.
The PDF is:
$$\Pr (Y = k)=\frac{\alpha^ke^{-e^\alpha+1}B_k}{k!},\quad k = 0, 1, 2, \dots$$
where $\alpha>0$, and $B_k$ are the Bell numbers (i.e., unique partitions of a set).
The R package fndemarqui/bellreg has a Stan implementation.