The statistical programs below are JavaScript implementations of statistical procedures that were justified in joint work with Mark Finkelstein and Howard G. Tucker. The objective of the research was to produce confidence intervals with a guaranteed coverage probability. This means that the confidence level of the interval found is provably at least as large as the specified level. (This property does not hold for many traditional intervals whose justification rests on asymptotic theory.) Details regarding the theory behind these procedures can be found in published journal articles. Use these programs at your own risk.
The theory underlying the first set of programs can be found in the paper Conservative Confidence Intervals for a Single Parameter by Mark Finkelstein, Howard G. Tucker and Jerry Alan Veeh, which appeared in Communications in Statistics: Theory and Methods volume 29 #8 pages 1911-1928 (2000).
Maximum likelihood estimator of, and conservative confidence intervals for, the binomial success probability.
Maximum likelihood estimator of, and conservative confidence intervals for, the binomial number of trials.
Maximum likelihood estimator of, and conservative confidence intervals for, the number of successes in a population (when sampling without replacement).
Maximum likelihood estimator of, and conservative confidence intervals for, the population size (when sampling without replacement).
The theory underlying the next program 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).
Maximum likelihood estimator of, and conservative confidence intervals for, the number of colors in the equiprobable coupon collector's problem.
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