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$\kappa$ and the stellar polytrope index n$n$. We compare also the Kaniadakis relation n=n(κ)$n=n\left(\kappa \right)$ with n=n(q)$n=n\left(q\right)$ proposed in the Tsallis framework.