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Probability distributions supported on the simplex enjoy a wide range ofapplications across statistics and machine learning. Recently, a novel familyof such distributions has been discovered: the continuous categorical. Thisfamily enjoys remarkable mathematical simplicity; its density functionresembles that of the Dirichlet distribution, but with a normalizing constantthat can be written in closed form using elementary functions only. In spite ofthis mathematical simplicity, our understanding of the normalizing constantremains far from complete. In this work, we characterize the numerical behaviorof the normalizing constant and we present theoretical and methodologicaladvances that can, in turn, help to enable broader applications of thecontinuous categorical distribution. Our code is available athttps://github.com/cunningham-lab/cb_and_cc/.

On the Normalizing Constant of the Continuous Categorical Distribution