I am trying to generate random numbers in Wigner semi-circle distribution. Since this one does not have the analytical solution for the inverse function of the pdf. I wonder if anyone familiar with a standard way to generation random numbers (RNs) follow this distribution and what are the pros and cons for each method.
My initial guess from what I have researched is, I can use the rejection method or sample method on the uniform distributive random numbers to get the Wigner semi-circle one.
Previously, I have generated normally distributive RNs from uniformly distributive RNs using the Box-Muller transformation. Even I am not a statistics major, it was pretty straight forward process. However, I am having hard time grasp my head around other distributions, specifically this Wigner semi-circle.
Any instructions or source recommendations will be highly appreciated. Thank you.