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A New Confidence Interval for the Mean of a Bounded Random Variable
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A New Confidence Interval for the Mean of a Bounded Random Variable
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We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the mean with high probability for all distributions on a bounded interval, for all samples sizes, and for all confidence levels. This new method provides confidence intervals that are competitive with those produced using Student's t-statistic, but does not rely on normality assumptions. In particular, its only requirement is that the distribution be bounded on a known finite interval.
Forward citations
Cited by 2 Pith papers
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An Exact Distribution-Free Test for Means of Nonnegative Random Variables
K(X) formed from uniform Dirichlet weights is a valid finite-sample distribution-free p-value for H0: EXi≤1 for all independent nonnegative Xi, proving Gaffke's conjecture.
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On the Order-Conditional Optimality of Gaffke's Bound
Gaffke's bound is Buehler-optimal within the class of lower confidence bounds that induce its own sample ordering, for the maximum marginal mean of independent nonnegative variables.
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