I have closed form moment-generating function and characteristic function of a distribution, which describes waiting time of a continuous univariate random process. However, I cannot analytically invert the characteristic function to get PDF.
Now, I have run simulations of the original process in order to verify that my model adequately describes the process. Because data in this case are simulated, I exactly know model parameters. Therefore, I am not interested in parameter estimation for now.
By eyeballing histogram of simulated data and numerically computed PDF, my model seems to fit the data very well. However, I want to say something more concrete and quantitative. Is there any goodness-of-fit test with arbitrary distribution, whose PDF and CDF are not analytically available? If not, what other approaches can I take?