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