# A New Confidence Interval for the Mean of a Bounded Random Variable

arXiv: https://arxiv.org/abs/1905.06208 · HTML: https://mlsanity.com/paper/1905.06208/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 4 of 4)

- [Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions](https://mlsanity.com/paper/2212.13629/) (2022)
- [On the Provable Performance Guarantee of Efficient Reasoning Models](https://mlsanity.com/paper/2510.09133/) (2025)
- [Learning Fair Representations with High-Confidence Guarantees](https://mlsanity.com/paper/2310.15358/) (2023)
- [On the Order-Conditional Optimality of Gaffke's Bound](https://mlsanity.com/paper/2607.22971/) (2026)

## Abstract (arXiv)

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.