A Fuzzy Approach for Randomized Confidence Intervals
Methodology
2026-01-01 v1
Abstract
We propose randomized confidence intervals based on the Neyman-Pearson lemma, in order to make them more broadly applicable to distributions that do not satisfy regularity conditions. This is achieved by using the definition of fuzzy confidence intervals. These intervals are compared with methods described in the literature for well-known distributions such as normal, binomial, and Poisson. The results show that in high-variance situations, the new intervals provide better performance. Furthermore, through these intervals, it is possible to compute a lower bound for the expected length, demonstrating that they achieve the minimal maximum expected length for a Bernoulli trial observation.
Cite
@article{arxiv.2512.23866,
title = {A Fuzzy Approach for Randomized Confidence Intervals},
author = {Carlos Henrique Trigo Nasser Felix and Nancy Lopes Garcia and Alex Rodrigo dos Santos Sousa},
journal= {arXiv preprint arXiv:2512.23866},
year = {2026}
}