Various algorithmic estimations of parametric distributions using the first four moments have become a standard practice in applied statistics and metrology. It was found that the distribution fitting algorithms have the following limitations: 1) they support the use of only up to four moments; and 2) the studied algorithms covered only unimodal distributions.
Here, we provide a stable moment-based maximum entropy (MaxEnt) method for parametric distribution fitting, which overcomes the aforementioned limitation. The Maxent method has also been shown to be superior to other distribution fitting techniques, specifically for the evaluation of expanded uncertainty in measurements.
Minor part of the results on the performance of the MaxEnt method has been published in 2017 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) in Torino, Italy. Therefore, the best citation for using the presented MaxEnt algorithm are:
A. Rajan, Y. C. Kuang, M. P.-L. Ooi, S. Demidenko, and H. Carstens “Moments and Maximum Entropy Method for Expanded Uncertainty Estimation in Measurements,” IEEE Access, 2017.
A. Rajan, Y. C. Kuang, M. P.-L. Ooi, and S. Demidenko, "Moments and maximum entropy method for expanded uncertainty estimation in measurements," in International Instrumentation and Measurement Technology Conference (I2MTC), 2017 IEEE, Torino, Italy, 2017.