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We derive the sampling probability density function (pdf) of an ideallocalized random electromagnetic field, its amplitude and intensity in anelectromagnetic environment that is quasi-statically time-varying statisticallyhomogeneous or static statistically inhomogeneous. The results allow for theestimation of field statistics and confidence intervals when a single spatialor temporal stochastic process produces randomization of the field. Results forboth coherent and incoherent detection techniques are derived, for Cartesian,planar and full-vectorial fields. We show that the functional form of thesampling pdf depends on whether the random variable is dimensioned (e.g., thesampled electric field proper) or is expressed in dimensionless standardized ornormalized form (e.g., the sampled electric field divided by its sampledstandard deviation). For dimensioned quantities, the electric field, itsamplitude and intensity exhibit different types of  Bessel $K$ sampling pdfs, which differ significantly from the asymptoticGauss normal and $\chi^{(2)}_{2p}$ ensemble pdfs when $\nu$ is relativelysmall. By contrast, for the corresponding standardized quantities, Student $t$,Fisher-Snedecor $F$ and root-$F$ sampling pdfs are obtained that exhibitheavier tails than comparable Bessel $K$ pdfs. Statistical uncertaintiesobtained from classical small-sample theory for dimensionless quantities areshown to be overestimated compared to dimensioned quantities. Differences inthe sampling pdfs arising from de-normalization versus de-standardization areobtained.

Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems