Q:

Reflecting the Polya-Aeppli distribution

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.

A:

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}]]

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. *)

