  We study the Kodaira dimension of a real parallelizable manifold $M$, with an
almost complex structure $J$ in standard form with respect to a given
parallelism. For $X = (M, J)$ we give conditions under which
$\operatorname{kod}(X) = 0$. We provide examples in the case $M = G \times G$,
where $G$ is a compact connected real Lie group. Finally we describe
geometrical properties of real parallelizable manifolds in the framework of
statistical geometry.
