2 problems

Let $\mathbf{M}_{r,N}(\alpha,\theta_{0},\beta,\theta)$ be the number of clusters with frequency $r$ in a sample of size $N$ under the hierarchical Pitman–Yor process, and let…

Let ${\bf M}_n$ have the multinomial distribution ${\cal M}(n,\theta)$, where $\theta=(\theta_1,\theta_2,\ldots)$ satisfies … and let $Y_n^{(d)}$ denote the number of urns containi…