Let's say I have some PDF $D$ that I can sample from. I would instead like to sample values from $Inv(D)$. I have that the $D$ is only positive within the bounds $[a,b]$ and is bounded above and below by $[c,d]$. That is, the domain of $D$ is a subset of $[a,b]$ and the range of $D$ is a subset of $[c,d]$. How can I go about sampling from $Inv(D)$?
I'm not sure that this is the standard use of "inverse" with respect to a distribution, so the image below should give an idea of what I mean. I can readily sample from the shaded region in the top distribution, but what I want is to sample from the shaded region in the bottom distribution.
Update: I am looking to sample a single value from this inverse distribution at random intervals. My application is a setting wherein I have an agent exploring a domain. The agent models the areas of the value space that it has already explored, currently with a maximum-likelihood Gaussian of the values the agent has observed. Thus to pick a value of an unexplored area, the agent needs to periodically sample from the "inverse" of this Gaussian. Right now I'm just sampling from a uniform distribution and seeing decent results, so speed is more important to me than accuracy.