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How would I go about reflecting the Polya-Aeppli distribution in Mathematica about a y-axis (switching left and right) while keeping the command. The distribution will not allow negative parameters for k or theta. The main thing is I need a distribution with exactly the same properties, except the tail becomes skewed left instead of right. It just would be really convenient to keep the same command.

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    $\begingroup$ How about TransformedDistribution[-x, x \[Distributed] PolyaAeppliDistribution[θ, p]]? $\endgroup$ – Rahul Jan 11 '14 at 8:40
  • $\begingroup$ Thank you. The documentation agrees, but I'll have to figure out how to plot it. I'm going to try to extend on mathematica.stackexchange.com/questions/4760/…, but this is very new to me. $\endgroup$ – Teg Jan 11 '14 at 17:36
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Not sure if I've understand your question, but if you just need the reflected plot, you can try:

With[{θ = 7, p = 1/4, m = -35}, 
      DiscretePlot[PDF[PolyaAeppliDistribution[θ, p], -x], {x, m, 0}]]

enter image description here

The method suggested by @Rahul Narain is also available:

With[{θ = 7, p = 1/4, m = -35}, 
 DiscretePlot[PDF[TransformedDistribution[-y, 
    y \[Distributed] PolyaAeppliDistribution[θ, p]], x], {x, m, 0}]]
(* The plot is same as the former so let me omit it. *)
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