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.
Not sure if I've understand your question, but if you just need the reflected plot, you can try:
The method suggested by @Rahul Narain is also available: