Distribution of a Sum of Waiting Times in Coupon Collection

摘要

The problem of approximating the distribution of the sum of n times to collect all of M coupons is considered. The Edgeworth expansion is obtained to terms of order n to the -3/2 power. Tables are given for M = 30, n = 8, 16, and 32, of the accuracy of the Edgeworth expansion for the cumulative distribution function approximately (because of discreteness) .001, .01, .1, .9, .99, and .999. (Author)