A New Confidence Interval for the Mean of a Bounded Random Variable
This provides a more robust statistical tool for researchers and practitioners dealing with bounded data where normality cannot be assumed.
The paper tackles the problem of constructing confidence intervals for the mean of bounded random variables without normality assumptions, resulting in intervals competitive with Student's t-statistic while requiring only known bounds on the distribution.
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.