Higher-Order Statistics for Stochastic Electromagnetic Interactions: Applications to a Thin-Wire Frame

Abstract

Abstract-Uncertainties in an electromagnetic observable, that arise from uncertainties in geometric and electromagnetic parameters of an interaction configuration, are here characterized by combining computable higher-order moments of the observable with higher-order Chebychev inequalities. This allows for the estimation of the range of the observable by rigorous confidence intervals. The estimated range is then combined with the maximum-entropy principle to arrive at an efficient and reliable estimation of the probability density function of the observable. The procedure is demonstrated for the case of the induced voltage of a thin-wire frame that has a random geometry, is connected to a random load, and is illuminated by a random incident field.

Mode-stirred reverberation chambers: A paradigm for spatio-temporal complexity in dynamic electromagnetic environments

“…Moreover, compound exponential (CE) PDFs arose in [14] (see that paper for definitions of α i and β i ), on the basis of partial 3D polarization of random EM free fields. While CE PDFs also produce better agreement with experiment compared to χ 2 6 PDFs at relative long wavelengths, their origin lies instead in the statistical anisotropy in random fields (especially near deterministic [16,[40][41][42] and stochastic [43][44][45][46][47] EM boundaries), unlike Bessel K PDFs that do not discriminate between spatial directions (although a generalization to statistically anisotropic fields exists [32, App. III]).…”