Technical Report CS0549

Title: The Coupon-Collector Problem Revisited
Authors: A. Boneh and M. Hofri
Abstract: A standard combinatorial problem calIs to estimate the expected number of purchases of coupons which may be of m different types, needed to complete the collection. Generalizing this problem by letting the coupons be obtained with an arbitrary probability distribution, and considezing other related processes, the problem has been found to model many practical situations. The usefulness of this model has been seriously hampered by the computational difficulties in obtaining any numerical results. cooceming moments or distributions. We show that the calculus of generating functions may be applied to the problem, answer numerous questions about the sampling process and demonstrate their numerical efficiency.
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