论文标题
优惠券收集器问题中的K-tons数量
The number of k-tons in the coupon collector problem
论文作者
论文摘要
考虑一下优惠券收集器问题，其中每个品牌的谷物品牌都包含优惠券，并且有不同类型的优惠券。假设包含特定类型优惠券的盒子的概率为$ 1/n $，并且我们一直购买盒子，直到我们收集每种类型的至少$ m $票券为止。对于$ k \ geq m $，如果我们看到所有优惠券的$ m $副本时，我们会看到$ k $ th的特定优惠券。在这里，我们确定在有限范围内的任何$ k $的$ m $副本之后，鉴于任何固定的$ m $，在收集了$ k $ tons的渐近分布。我们还确定了此类$ K $的渐近关节概率分布以及收集的优惠券总数。
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.
