Estimating a Dirichlet distribution

Abstract

The Dirichlet distribution and it's compound variant, the Dirichlet-multinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the maximum-likelihood estimate of these distributions is not available in closed-form. This paper describes simple and efficient iterative schemes for obtaining parameter estimates in these models. In each case, a fixed point iteration and a Newton-Rhapson (or generalized Newton-Rhapson) iteration is provided.