Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or low) scores as anomalies. This presents a practical limitation on the applicability of such methods, since most methods are sensitive to the choice of the threshold, and it is challenging to set optimal thresholds. The issue is exacerbated in a streaming scenario, where the optimal thresholds vary with time. We present a probabilistic framework to explicitly model the normal and anomalous behaviors and probabilistically reason about the data. An extreme value theory based formulation is proposed to model the anomalous behavior as the extremes of the normal behavior. As a specific instantiation, a joint nonparametric clustering and anomaly detection algorithm (INCAD) is proposed that models the normal behavior as a Dirichlet process mixture model. Results on a variety of datasets, including streaming data, show that the proposed method provides effective and simultaneous clustering and anomaly detection without requiring strong initialization and threshold parameters.