In a mathematical model I've written, values for one of the parameters (call this parameter $b$) are sampled uniformly from trial to trial from a Gabor function.
The Gabor function $G$ is as follows:
\begin{align} b_x = G(x) =h e^{-(wx)^2}\sin(wx). \end{align}
Here, $x$ is an independent variable selected from a uniform distribution from trial to trial. $h$ and $w$ are fixed.
My question is, what is the PDF for my parameter $b$?
Note that the Gabor function integrates to 0 across its domain (which is $-\pi$ to $\pi$). It is not one-to-one.