This report describes an approach for generating a simulated population of plausible nuclear threat radiation signatures spanning a range of variability that could be encountered by radiation detection systems. In this approach, we develop a statistical model for generating random instances of smuggled nuclear material. The model is based on physics principles and bounding cases rather than on intelligence information or actual threat device designs. For this initial stage of work, we focus on random models using fissile material and do not address scenarios using non-fissile materials. The model has several uses. It may be used as a component in a radiation detection system performance simulation to generate threat samples for injection studies. It may also be used to generate a threat population to be used for training classification algorithms. In addition, we intend to use this model to generate an unclassified 'benchmark' threat population that can be openly shared with other organizations, including vendors, for use in radiation detection systems performance studies and algorithm development and evaluation activities.