On Birthday, Collectors', Occupancy and Other Classical Urn Problems
本文通过嵌入泊松过程，统一处理了生日问题、收集者问题等经典瓮问题，推导出精确和渐近结果，并讨论了其他抽取方案。
Summary An urn contains r different balls. Balls are drawn with replacement until any k balls have been obtained at least m times each. How many draws are necessary? How many balls have been drawn exactly v times? Special cases of such problems are often named as birthday, collectors', dixie cup or occupancy problems. This paper presents a unified approach to such problems by imbedding in Poisson processes. In this way we see that many classical urn problems are closely related to properties of order statistics and extreme values from the gamma distribution. Both exact and asymptotic results are derived. Finally, a brief discussion is given on other drawing schemes.