The emission of electromagnetic radiation by localized complex electric charge and current distributions is studied. A statistical formalism in terms of general dynamical multipole fields is developed. The appearing coefficients are treated as stochastic variables. Hereby as much as possible a priori physical knowledge is exploited. First results of simulated statistical electromagnetic fields as a function of position are presented. Sampling this field at one point approximates its resulting probability density. © 2007 The American Physical Society.