The Dirichlet-Gamma-Poisson model, a new model of repeated events, is a means of understanding how the multivariate distribution of crimes reported in city samples of the National Crime Survey can be used to make inferences about exposure to high crime situations. The model is based on the assumption that persons have a constant chance of being victimized over time but that not all persons have the same chance. This research indicates how the multivariate distribution of various types of crimes reported in one time period can be used to make inferences about victim liability, which presumably corresponds closely to victim exposure. The simple Poisson model can be generalized into the univariate Gamma-Poisson model. This model has been shown by Nelson (1980a) to be compatible with the lifestyle/exposure theory of victimization and to be capable of generating the univariate distribution of many different types of victimizations. Three multivariate Gamma-Poisson models are developed and fitted to distributions of four specific types of victimizations reported in the city samples. The Dirichlet-Gamma-Poisson model is the most general of these models. In addition to estimating individual liability rates of specific types of crimes, the model predicts chances that specific types of crimes will occur in the future. The model is expected to be useful in describing many different kinds of social phenomena. The appendixes contain the estimation of m and k in the Gamma-Poisson model and the estimation of the Dirichlet parameters. Tabular data, mathematical equations, and 19 references are provided.