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add Bell distribution #3172

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@wpetry

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@wpetry

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.

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