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.
Sy, O. O., Beurden, van, M. C., Michielsen, B. L., Vaessen, J. A. H. M., & Tijhuis, A. G. (2012). Higher-order statistics for stochastic electromagnetic interactions: applications to a thin-wire frame. Progress In Electromagnetics Research B, 41, 307-332. https://doi.org/10.2528/PIERB12042104