Analysis of Complex-Valued Quantities in Magnitude and Phase

In the evaluation of uncertainty related to complex-valued measurements, coverage factors must be derived in order to account for the probability for the measurand to lie within a given uncertainty region, generally of elliptical form (Ridler, 1998). These coverage factors are dependent on the type of two-dimensional probability density function (PDF) assumed. Traditional approaches assume bivariate normal distribution in the real and imaginary components. In this paper a new definition for the PDF is explored, which assumes Gaussian distribution for the magnitude and uniform distribution for the phase. This so-called Gaussian magnitude PDF is compared with the bivariate normal distribution in real and imaginary. For both models, coverage factors for the usual confidence level of 95% are derived