Moments and maximum entropy method for expanded uncertainty estimation in measurements

The normal approximation and Monte Carlo simulation methods are widely used in the metrology to evaluate the expanded uncertainty, whereby the latter method is known to be the most robust and reliable. In some cases, however, (e.g., when the probability distribution is not known a priori) different frameworks may be desired as an alternative to the aforementioned techniques. One of them is commonly used in metrology-it is the moment (or cumulant)-based method. In view of that, and specifically for the scope of the expanded uncertainty estimation, this paper studies the theoretical viability of using high-order moments. It also analyzes the performance of a relatively new parametric distribution fitting technique known as the maximum entropy method. The discussions in the paper substantiate the confident application of the moment-based approach among practitioners. Furthermore, the results from the performance analysis of the maximum entropy method could guide practitioners in selecting a distribution fitting algorithm that best suits their respective systems.