Fiducial intervals for the magnitude of a complex-valued quantity

Abstract

This paper discusses a fiducial approach for constructing uncertainty intervals for the distance between k normal means and the origin. When k = 2 this distance is equivalent to the magnitude of a complex-valued quantity. A simulation study was conducted to assess the frequentist performance of the proposed fiducial intervals and to compare their performance with the methods from the Guide to the Expression of Uncertainty in Measurement and from Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’—Propagation of Distributions using a Monte Carlo Method. Our results indicate that the fiducial intervals generally outperform the GUM and GUM Supplement 1 methods with respect to frequentist coverage probabilities. Computer programs for calculating the fiducial intervals, written using open-source software, are listed.