Asymptotics for the random coupon collector problem
Suppose that \(N\) objects are sampled independently with replacement until all objects have been seen. Let this happen at trial \(T\). To each object there is a drawing probability; these probabilities are proportional to iid observations of a positive random variable with Laplace transform \(g(t)\). The mean \(E(T)\) is expressed in \(g(t)\). Using this the asymptotics of \(E(T)\) is studied when \(N\) tends to infinity. The asymptotics is typically determined by the behaviour of \(g(t)\) for large \(t\) or equivalently by the distribution function close to 0.
scientific article; zbMATH DE number 1326307