In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the number of parameters. Random vectors with a GD distribution are completely neutral.[1]
The density function of is
where we define . Here denotes the Beta function. This reduces to the standard Dirichlet distribution if for ( is arbitrary).
For example, if k=4, then the density function of is
where and .
Connor and Mosimann define the PDF as they did for the following reason. Define random variables with . Then have the generalized Dirichlet distribution as parametrized above, if the are independent beta with parameters , .