Supplement 1.docx

To date, the evaluation of expanded uncertainty is handled exclusively by Monte Carlo (MC) method. However, there are cases where MC cannot be applied and thus alternative methods are necessary. One typical scenario is when type-A evaluation is required. Currently, the only other mainstream solution is to identify an appropriate distribution based on the information obtained from the high-order moments of the data.

On the other hand, there is currently no comprehensive test distributions that exist to standardize the performance evaluation of moment-based distribution fitting techniques. Without such benchmark test distributions, it is not possible to compare the performance of one technique to the other. Therefore, while the fitting techniques can be reliably used for distributions that are close to the previously tested distributions, there is insufficient information on their performance for other distributions.

For that reason, the objective of the set of distributions in given here is to establish a benchmark distribution set and a framework for performance comparison between various parametric distribution fitting methods especially for expanded uncertainty estimation. A fitting technique can be assessed easily using the framework shown in the reference article given under References. The Distribution List and Distribution Solution can be obtained from this uploaded supplementary document.