  It has been shown in the literature that effective gravitational constants,
which are derived from Verlinde's formalism, can be used to introduce the
Tsallis and Kaniadakis statistics. This method provides a simple alternative to
the usual procedure normally used in these non-Gaussian statistics. We have
applied our formalism in the Jeans mass criterion of stability and in the free
fall time collapsing of a self-gravitating system where new results are
obtained. A possible connection between our formalism and deviations of
Newton's law of gravitation in a submillimeter range is made.
