Benchmark Test Distributions for Expanded Uncertainty Evaluation Algorithms

Expanded uncertainty estimation is normally required for mission-critical applications, e.g., those involving health and safety. It helps to get a distribution range of the required confidence level for the uncertainty evaluation of a system. There are a number of available techniques to estimate the expanded uncertainty. However, there is currently no commonly accepted benchmark test distribution set adopted to compare the performances of different techniques when they are used to estimate the expanded uncertainty. Without such a common benchmarking platform, the relative reliability of a particular technique in comparison to other techniques can be untrustworthy. To address the shortcoming, this paper proposes a set of analytically derived benchmark test distributions. It goes on to show the benefits of using them by comparing the performance of existing distribution fitting techniques when applied to the moment-based expanded uncertainty evaluation. The most commonly used moment-based distribution fitting techniques, such as Pearson, Tukey's gh, Cornish-Fisher expansion, and extended generalized lambda distributions, are employed as test cases in this paper. The test distribution set proposed in this paper provides a common benchmarking platform for metrologists intending to assess the performance of different expanded uncertainty estimation techniques. Results from the performance comparison would help practitioners to make a better choice of a distribution fitting technique that would best suit their respective systems.