Let's say i want to fit a certain exotic distribution using maximum likelihood estimation. However, i have no access to the theoretical probability density function to retrieve the likelihood (it is an exotic distribution). On the other hand, i can use a model to simulate the process that is supposed to give rise to this exotic distribution, and therefore, i can have the simulation return a "simulated" probability density function (pdf) given some parameters.
The question is: can i use this simulated pdf to retrieve the likelihood of my data? I don't see any immediate problem with doing this, if the simulation is based enough samples so that the simulated pdf gets close enough to the theoretical pdf (to which i have no access).
I am mainly wondering whether this approach is correct? Or am i missing something?
Thanks in advance!