DirichletDistribution

The Dirichlet distribution on the $(k-1)$ -simplex with concentration parameters $\alpha_1,\ldots,\alpha_k$ .

DirichletDistribution({alpha1, ..., alphak})distribution on the (k-1)-simplex, parameterised over the first k-1 coordinates.

Typed signatures

Type	Package	Applies
`(list<real>) -> distribution`	`statistics`	always

Domain: Statistics

Details

Wolfram's own parameterisation is over the FIRST $k-1$ coordinates: $PDF$ takes a $(k-1)$ -list $\{x_1,\ldots,x_{k-1}\}$ , with $x_k := 1-\sum_{i<k} x_i$ implicit, and $Mean$ / $Variance$ are each $(k-1)$ -lists — $\alpha_k$ 's own coordinate is never reported directly (confirmed from Wolfram's own DirichletDistribution reference page: Mean/Variance examples for a 3-parameter call return length-2 lists).
$PDF(x) = \left(\prod_{i=1}^k x_i^{\alpha_i-1}\right) / B(\alpha)$ , $B(\alpha) = \prod_i \Gamma(\alpha_i) / \Gamma(\sum_i \alpha_i)$ .
$Mean_i = \alpha_i / \sum \alpha$ for $i = 1,\ldots,k-1$ .
$Variance_i = \alpha_i(\sum\alpha - \alpha_i) / \left((\sum\alpha)^2(\sum\alpha+1)\right)$ for $i = 1,\ldots,k-1$ .
CDF and RandomVariate are not implemented for this head (out of scope for this batch) — stay unevaluated.