Limit distributions for the problem of collecting pairs - Mathematics > Statistics Theory

Abstract: Let $N n=\{1,2, .,n\}$. Elements are drawn from the set $N n$ withreplacement, assuming that each element has probability $1-n$ of being drawn.We determine the limiting distributions for the waiting time until the givenportion of pairs $jj$, $j\in N n$, is sampled. Exact distributions of somerelated random variables and their characteristics are also obtained.