In some service operations settings, data are available only for system outputs but not the constituent input models. Examples are service call centers and patient flows in clinics, where sometimes only the waiting time or the queue length data are collected for economic or operational reasons, and the data on the 'input distributions', namely interarrival and service times, are limited or unavailable. In this paper, we study the problem of estimating these input distributions with only the availability of the output data, a problem usually known as the inverse problem, and we are interested in the context where stochastic simulation is required to generate the outputs. We take a nonparametric viewpoint, and formulate this inverse problem as a stochastic program by maximizing the entropy of the input distribution subject to moment matching. We then propose an iterative scheme via simulation to approximately solve the program.