We introduce a novel parametric BRDF model that can accurately encode a wide variety of real-world isotropic BRDFs with a small number of parameters. The key observation we make is that a BRDF may be viewed as a statistical distribution on a unit hemisphere. We derive a novel directional statistics distribution, which we refer to as the hemispherical exponential power distribution, and model an isotropic BRDF with a mixture of it. The novel directional statistics BRDF model allows us to derive a canonical probabilistic method for estimating its parameters including the number of components. We show that the model captures the full spectrum of real-world isotropic BRDFs with accuracy comparable to non-parametric models but with a much more compact representation. We also experimentally show that the model achieves better accuracy with less measurements compared with such non-parametric models. We further demonstrate the advantages of the novel BRDF model by showing its use for reflection component separation and for exploring the space of isotropic BRDFs.