DirichletAnteile
DirichletAnteile, or Dirichlet shares, denotes the components of a random vector that lies on the probability simplex. If X = (X1, ..., XK) follows a Dirichlet distribution with parameters α = (α1, ..., αK) with αi > 0, then each Xi is nonnegative and the sum of all components equals 1. The vector X is commonly described as consisting of DirichletAnteile.
The Dirichlet distribution Dirichlet(α) is a multivariate generalization of the Beta distribution. Its probability density on
Key properties: The expected value of each DirichletAnteil is E[Xi] = αi / α0. The variance is Var[Xi]
Common uses and significance: DirichletAnteile appear as the conjugate prior for multinomial likelihoods in Bayesian statistics,
Historically, the Dirichlet distribution is named after Johann Peter Gustav Lejeune Dirichlet, with the component shares