Fiducial Intervals for the Magnitude of a Complex-Valued Quantity
Chih-Ming Wang, Hariharan K. Iyer
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. Uncertainty intervals for the magnitude based on 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 have been shown to have inadequate long-run success rate. A simulation study indicates that the fiducial intervals have good frequentist performance. Computer programs for calculating the fiducial intervals, written using open-source software, are listed.