Site LogoThe Coupon Collector's Colors


This JavaScript program computes the maximum likelihood estimator of, and confidence intervals for, the number of unknown colors in the equiprobable coupon collector's problem. A population contains an unknown number of different types of items, here referred to as colors. There are an equal number of items of each color. Items are drawn one at a time with replacement from the population. In these draws the number of different colors obtained is observed. The objective is to estimate, and find confidence intervals for, the number of different colors in the population. One application of this problem is the estimation of the size of a wildlife population. The theory underlying the computations can be found in the paper Confidence Intervals for the Number of Unseen Types by Mark Finkelstein, Howard G. Tucker, and Jerry Alan Veeh, which appeared in Statistics and Probability Letters volume 37 pages 423-430 (1998). The annotated source code is available


Observed number of colors in the sample
Sample Size
Confidence Level (%)

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