Non-Gaussian statistics, Maxwellian derivation and stellar polytropes

In this letter we discuss two aspects of non-Gaussian statistics. In the first, we show that Maxwell’s first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. In the second, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter κ and the stellar polytrope index n . We compare also the Kaniadakis relation n = n ( κ ) with n = n ( q ) proposed in the Tsallis framework.