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## posterior predictive distribution of negative binomial, pareto?

what is the posterior predictive distribution of a negative binomial, with a conjugate prior beta distribution placed over the probability? $r$ is assumed to be fixed. Definition is as on Wikipedia, where $p$ is probability of success (not failure), $r$ is the number of failures till the experiment stops, and the support starts at 0.

what about the posterior predictive distribution of a pareto distribution, with a conjugate prior gamma distribution placed over the shape $k$? Minimum $x_m$ is assumed to be fixed.

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 Is $r$ assumed to be known? $\:$ Is $x_m$ assumed to be known? $\:$ Regardless of what the answers $\hspace{0.9 in}$ to those questions are, I suspect your question is not appropriate here and should be asked at math.stackexchange.com $\;\;$ – Ricky Demer Mar 22 2012 at 3:22