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.
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.
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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.