I have the following pdf: $$ f(x) = C x^d I_0\left(b \sqrt{- \log\left(\frac{x}{A}\right)}\right)$$ for $0 < x \leq A$, $C$ is a normalizing constant, $b$, $d$ are constants, and $I_0$ is the modified Bessel function of first kind of order $0$.
I know that in order to sample from $f$, I can use:
- Inverse CDF method
- Acceptance rejection technique
The problem with the first is that I was enable to compute the CDF, and thus not able to inverse it. Regarding the second, I know that I have to find a pdf $g$ such that the ratio of pdfs is upper bounded by some constant. The problem is that, I'm not familiar with the modified Bessel function of first kind, so I was hoping if you could help me find $g$ or if you know other sampling techniques that may be helpful in this case.
Thanks!