Abstract: The extreme Fisher information (EFI) is originally a measure within the theory of extreme physical information (EPI). In measurement activities, it is hard to accurately and efficiently identify and compensate every effect in measurement and evaluate the incompleteness of the measurement results. So we propose to employ the probability density functions (PDFs) derived from the EFI for estimating the boundary information of the measurement results, that is, the associated measurement uncertainty. The proposed method can characterize the measurement uncertainty more dynamically, with considering the different behaviors of the uncertainty effects and the law governing the system under measurement at the same time. The proposed approach yields the possible distribution of the measurement result in a more practical way rather than the pure mathematical approach, which is more applicable. Finally, the effectiveness of the proposed EFI method is demonstrated by the numerical results of two practical instances.