Perpetuity property of the Dirichlet distribution

Pawel Hitczenko, Gerard Letac

Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\sim \mathcal{D}(a_0,...,a_d),$ such that $\mathrm{Pr}(B=(0,...,0,1,0,...,0))=a_i/a$ wi…