This paper extends the Stochastic Method of Cuts (SMoC) to approximate of the Macroscopic Fundamental Diagram (MFD) of urban networks and uses Maximum Likelihood Estimation (MLE) method to estimate the model parameters based on empirical data from a corridor and 30 cities around the world. For the corridor case, the estimated values are in good agreement with the measured values of the parameters. For the network datasets, the results indicate that the method yields satisfactory parameter estimates and graphical fits for roughly 50\% of the studied networks, where estimations fall within the expected range of the parameter values. The satisfactory estimates are mostly for the datasets which (i) cover a relatively wider range of densities and (ii) the average flow values at different densities are approximately normally distributed similar to the probability density function of the SMoC. The estimated parameter values are compared to the real or expected values and any discrepancies and their potential causes are discussed in depth to identify the challenges in the MFD estimation both analytically and empirically. In particular, we find that the most important issues needing further investigation are: (i) the distribution of loop detectors within the links, (ii) the distribution of loop detectors across the network, and (iii) the treatment of unsignalized intersections and their impact on the block length.