The Dirichlet distribution and its 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-Raphson (or generalized Newton-Raphson) iteration is provided.<\/p>\n","protected":false},"excerpt":{"rendered":"
The Dirichlet distribution and its 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 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