The number of k-tons in the coupon collector problem

J. C. Saunders

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arXiv · 2005.08915

The number of k-tons in the coupon collector problem

J. C. Saunders

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Abstract

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 $k\geq m$ 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.

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J. C. Saunders. 2020-05-18. The number of k-tons in the coupon collector problem. https://arxiv.org/abs/2005.08915

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