论文信息 - Siobhan's Problem: The Coupon Collector Revisited

Siobhan's Problem: The Coupon Collector Revisited

Abstract This article considers from an empirical point of view the convergence of the distribution function for the waiting time in the classical coupon collector's problem. In addition, the application of the distribution in testing for “randomness” in the decimal expansions of π and e is considered. Some remarks are also made on the inverse problems: namely, given i distinct objects obtained in sampling at random with replacement m times from some population, how many distinct objects are there in the population?

Brian P. Dawkins

[1] Olga Taussky. Statistical Treatment of Values of First 2,000 Decimal Digits of e and of /pi Calculated on the ENIAC , 1950 .

[2] John Riordan,et al. Introduction to Combinatorial Analysis , 1959 .

[3] Patrick Billingsley,et al. Asymptotic Distributions for the Coupon Collector's Problem , 1965 .

[4] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[5] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .

[6] B. Rosén,et al. Asymptotic normality in a coupon collector's problem , 1969 .

[7] Bengt Rosen. On the Coupon Collector's Waiting Time , 1970 .

[8] G. Seber,et al. The Estimation of Animal Abundance , 1975 .

[9] Pranab Kumar Sen,et al. Invariance Principles for the Coupon Collector's Problem: A Martingale Approach , 1979 .

[10] L. Cook,et al. Estimating the Size of Animal Populations , 1982 .

[11] Frederick Mosteller,et al. Fifty Challenging Problems in Probability with Solutions , 1987 .

[12] Robert L. Mason,et al. A Brief History of the American Statistical Association, 1839-1989 , 1990 .