Copulas, Outliers, and Rogue States of Nonelliptic Fields and Energy in Electromagnetic Reverberation

An algorithm is developed for extracting the probability density function of nonelliptic Cartesian or vector stochastic fields and their energy from data. The probability density incorporates both linear and nonlinear dependence between the inphase (I-) and quadrature (Q-) components characterized by their I/Q copula density. Semiparametric elliptic copulas for data are found to differ significantly from nonparametric empirical copulas when the global I/Q dependence is moderate or weak, despite yielding the same marginal field distributions. Outliers of fields or energy are identified as local concentrations in their copula density near the center or vertices of its domain. The nonlinear I/Q dependence embodied by copulas provides a possible mechanism for generating rogue wave fields during stir step transitions in reverberation chambers. The inclusion of local I/Q dependence allows for an accurate estimation of extreme levels of field strength in testing for immunity, emissions, and fading, in support of the analysis of risk, confidence, and reliability in complex dynamic environments.