In this help file the response is assumed to be a $M$-column
matrix with positive values and whose rows each sum to unity.
Such data can be thought of as compositional data.
There are $M$ linear/additive predictors $\eta_j$.
The Dirichlet distribution is commonly used to model compositional
data, including applications in genetics.
Suppose $(Y_1,\ldots,Y_{M})^T$ is
the response. Then it has a Dirichlet distribution if
$(Y_1,\ldots,Y_{M-1})^T$ has density
$$\frac{\Gamma(\alpha_{+})}
{\prod_{j=1}^{M} \Gamma(\alpha_{j})}
\prod_{j=1}^{M} y_j^{\alpha_{j} -1}$$
where $\alpha_+=\alpha_1+\cdots+\alpha_M$,
$\alpha_j > 0$,
and the density is defined on the unit simplex
$$\Delta_{M} = \left{
(y_1,\ldots,y_{M})^T :
y_1 > 0, \ldots, y_{M} > 0,
\sum_{j=1}^{M} y_j = 1 \right}.$$
One has $E(Y_j) = \alpha_j / \alpha_{+}$, which are returned as the fitted values.
For this distribution Fisher scoring corresponds to Newton-Raphson.
The Dirichlet distribution can be motivated by considering the random variables
$(G_1,\ldots,G_{M})^T$ which are each independent
and identically distributed as a gamma distribution with density
$f(g_j)=g_j^{\alpha_j - 1} e^{-g_j} / \Gamma(\alpha_j)$.
Then the Dirichlet distribution arises when
$Y_j=G_j / (G_1 + \cdots + G_M)$.