A saddlepoint approximation for the collector's problem

This article presents several examples to show that a saddlepoint approxima tion to the distribution of the waiting time in the coupon collector's prob lem is very accurate. Also given here is a nice application of the saddlepo int approximation that may help statistics teachers to motivate their stude nts when teaching saddlepoint approximations. It illustrates the modern art of statistics relying on the computer and embodying both numeric and analy tic approximations.