We propose a new hierarchical Bayesian n-gram model of natural languages. Our model makes use of a generalization of the commonly used Dirichlet distributions called Pitman-Yor processes which produce power-law distributions more closely resembling those in natural languages. We show that an approximation to the hierarchical Pitman-Yor language model recovers the exact formulation of interpolated Kneser-Ney, one of the best smoothing methods for n-gram language models. Experiments verify that...