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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.


GUM, propagation of uncertainty, Supplement 1 to the GUM, uncertainty interval
Created December 19, 2008, Updated February 19, 2017