  Currently there is a concern about ability of the classical thermal
(Maxwellian) distribution to describe quasi-steady-state plasma in solar
atmosphere including active regions. In particular, other distributions have
been proposed to better fit observations, for example, kappa- and
$n$-distributions. If present, these distributions will generate radio
emissions with different observable properties compared with the classical
gyroresonance (GR) or free-free emission, which implies a way of remote
detecting these non-Maxwellian distributions in the radio observations. Here we
present analytically derived GR and free-free emissivities and absorption
coefficients for the kappa- and $n$-distributions and discuss their properties,
which are in fact remarkably different from each other and from the classical
Maxwellian plasma. In particular, the radio brightness temperature from a
gyrolayer increases with the optical depth $\tau$ for kappa-distribution, but
decreases with $\tau$ for $n$-distribution. This property has a remarkable
consequence allowing a straightforward observational test: the gyroresonance
radio emission from the non-Maxwellian distributions is supposed to be
noticeably polarized even in the optically thick case, where the emission would
have strictly zero polarization in the case of Maxwellian plasma. This offers a
way of remote probing the plasma distribution in astrophysical sources
including solar active regions as a vivid example.
