This manuscript is concerned with establishing a unified framework for concurrently generating data sets that include three major kinds of variables (i.e., binary, ordinal, and count) when the marginal distributions and a feasible association structure are specified for simulation purposes. The simulation paradigm has been commonly utilized in pharmaceutical practice. A central aspect of every simulation study is the quantification of the model components and parameters that jointly define a scientific process. When this quantification goes beyond the deterministic tools, researchers often resort to random number generation (RNG) in finding simulation-based solutions to address the stochastic nature of the problem. Although many RNG algorithms have appeared in the literature, a major limitation is that most of them were not devised to simultaneously accommodate all variable types mentioned above. Thus, these algorithms provide only an incomplete solution, as real data sets include variables of different kinds. This work represents an important augmentation of the existing methods as it is a systematic attempt and comprehensive investigation for mixed data generation. We provide an algorithm that is designed for generating data of mixed marginals; illustrate its operational, logistical, and computational details; and present ideas on how it can be extended to span more sophisticated distributional settings in terms of a broader range of marginal features and associational quantities.