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.

翻译：我们基于Neyman-Pearson引理提出随机置信区间，旨在使其更广泛地适用于不满足正则性条件的分布。这一目标通过采用模糊置信区间的定义实现。我们将这些区间与文献中针对正态分布、二项分布和泊松分布等常见分布描述的方法进行比较。结果表明，在高方差情况下，新区间具有更优的性能。此外，通过这些区间可以计算期望长度的下界，证明其在伯努利试验观测中达到了最小最大期望长度。