  In this letter we have shown that a possible connection between the LQG
Immirzi parameter and the area of a punctured surface can emerge depending on
the thermostatistics theory previously chosen. Starting from the
Boltzmann-Gibbs entropy, the Immirzi parameter can be reobtained. Using the
Kaniadakis statistics, which is an important non-Gaussian statistics, we have
derived a new relation between the Immirzi parameter, the kappa parameter and
the area of a punctured surface. After that, we have compared our result with
the Immirzi parameter previously obtained in the literature within the context
of Tsallis' statistics. We have demonstrated in an exact way that the LQG
Immirzi parameter can also be used to compare both Kaniadakis and Tsallis
statics.
