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. The red shaded region in figure (a) below shows where most test distributions used for performance assessment of the fitting techniques lie on skewness-kurtosis plot. The square and diamond points in the same figure show test distributions used for expanded uncertainty estimation using distribution fitting in literature. Therefore, while the fitting techniques can be reliably used for distributions that fall within the shaded region, there is insufficient information on their performance for distributions outside the shaded region.
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 figure (b) above. The Distribution List and Distribution Solution in figure (b) can be obtained by clicking on the buttons below.
|DISTRIBUTION LIST||DISTRIBUTION SOLUTION|
The button below provides a lookup table for solving g and h parameter for distribution fitting using Tukey's gh distribution
|LOOKUP TABLE FOR PARAMETER g AND h IN TUKEY'S GH DISTRIBUTION|
This webpage is deployed using webMathematica. Minor part of the
benchmark test distributions has been published in 2015 IEEE
International Instrumentation and Measurement Technology Conference
(I2MTC) in Pisa, Italy. Hence the best citation for using the
benchmark test distributions is:
Please send any your questions by emailing us.
Monash University Scholar
|Dr Kuang Ye Chow
Associate Head of School (Research Training)
|Dr Melanie Po-Leen Ooi
|Prof Serge Demidenko