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 variables with a GD distribution are neutral.
The density function of is
![\left[
\prod_{i=1}^{k-1}B(a_i,b_i)\right]^{-1}
p_k^{b_{k-1}-1}
\prod_{i=1}^{k-1}\left[
p_i^{a_i-1}\left(\sum_{j=i}^kp_j\right)^{b_{i-1}-(a_i+b_i)}\right]](http://upload.wikimedia.org/math/8/6/7/8670037fd9a237a6fd2d574253e5e345.png)
where we define . Here denotes the Beta function. This reduces to the standard Dirichlet distribution if for ( is arbitrary).
Wong gives the slightly more concise form for
where for and . Note that Wong defines a distribution over a dimensional space (implicitly defining ) while Connor and Mosiman use a dimensional space with . The remainder of this article will use Wong's notation.
Read more about Generalized Dirichlet Distribution: General Moment Function, Reduction To Standard Dirichlet Distribution, Bayesian Analysis, Sampling Experiment
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