Making inference in everyday life often requires people to make inferences about low frequency events. In the most extreme case, some types of object or event may have never been previously observed. An experiment is presented in which participants needed to infer the existence and number of unobserved event types, based solely on the frequency distribution of a set of observed events. Results indicate people's inferences are sensitive to the shape of the distribution over the observed events, even when the number of observed events and event types is held constant, and that people are able to infer abstract rules that describe entire classes of event distributions. Human inferences are shown to be similar to those made by a hierarchical Bayesian model.