Is there a continuous generalization of the Negative Binomial?

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Cody Ross

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Feb 6, 2015, 1:24:01 PM2/6/15
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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

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Feb 6, 2015, 1:43:48 PM2/6/15
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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

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Feb 6, 2015, 1:45:31 PM2/6/15
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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.

Cody Ross

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Feb 6, 2015, 4:02:32 PM2/6/15
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Jonah,

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