A Generalization of the Dirichlet Distribution

Abstract

This paper discusses a generalization of the Dirichlet distribution, the ‘hyperdirichlet’, in which various types of incomplete observations may be incorporated. It is conjugate to the multinomial distribution when some observations are censored or grouped. The hyperdirichlet R package is introduced and examples given. A number of statistical tests are performed on the example datasets, which are drawn from diverse disciplines including sports statistics, the sociology of climate change, and psephology.

Keywords

• Dirichlet distribution
• combinatorics
• R
• multinomial distribution
• constrained optimization