Is there a continuous generalization of the Negative Binomial?

[Cody Ross]

All,

I am stuck trying to deal with discrete (imputed data) parameters again (on the outcome variable). Missing data/ partially complete data points are imputed using a Poisson counting process, leading to a probability mass that doesn't conform to any simple distribution. I can fix the problem in a not-so-hacky way by fitting a scaled beta distribution to the estimates, but since this converts the integral values to continuous ones, I can't use a negative binomial outcome distribution. A gamma outcome distribution won't work because I have some true zeros.

Is there a continuous generalization of the Negative Binomial?

Is there any way to make this work in Stan, or am I going to have to relearn JAGS?

[Bob Carpenter]

I don't know any way to do this in Stan, but somebody
else might have some ideas. If you can't marginalize out
the Poissons, Stan won't work directly.

- Bob

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[Jonah]

Not sure if this is what you need or not, but for a continuous generalization of the negative binomial you might check out this paper by Chandra and Roy (link below). The title of the paper is A continuous version of the negative binomial distribution.

http://rivista-statistica.unibo.it/article/view/3635

[Cody Ross]

Jonah,

That might work, I'll give it a try.