2020/05/18 by JOHN C. SAUNDERS, Saunders, J. C. · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2005.08915
openalex publication_date 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider the coupon collector problem where each box of a brand of cereal contains a coupon and there are n different types of coupons. Suppose that the probability of a box containing a coupon of a specific type is 1/n and that we keep buying boxes until we collect at least m coupons of each type. For k≥ m call a certain coupon a k-ton if we see it k times by the time we have seen m copies of all of the coupons. Here we determine the asymptotic distribution of the number of k-tons after we have collected m copies of each coupon for any k in a restricted range, given any fixed m. We also determine the asymptotic joint probability distribution over such values of k and the total number of coupons collected.