  Let $k \geq 2$ be an integer. We prove that factorization of integers into
$k$ parts follows the Dirichlet distribution
$\text{Dir}\left(\frac{1}{k},\ldots,\frac{1}{k}\right)$ by multidimensional
contour integration, thereby generalizing the Deshouillers-Dress-Tenenbaum
(DDT) arcsine law on divisors where $k=2$. The same holds for factorization of
polynomials or permutations. Dirichlet distribution with arbitrary parameters
can be modelled similarly.
