Correct ordering in the Zipf-Poisson ensemble

Justin S. Dyer, Art B. Owen

We consider a Zipf--Poisson ensemble in which $X_i\sim\poi(Ni^{-α})$ for $\alpha >1$ and $N>0$ and integers $i\ge 1$. As $N\to \infty$ the first $n^{\prime }(N)$ random variables have their proper…