Abstract
Incomplete statistics, an important extension of the Boltzmann-Gibbs statistical distribution, was proposed few years back by Wang. The main point is that the formalism adopts an incomplete normalization condition given by , where q is a positive real parameter and pi is the probability of a determined microstate. In this paper, we have used this framework to derive a new relation between the Immirzi parameter, the q incomplete parameter and the area of a punctured surface. After that, we have compared our result to the Immirzi parameter previously obtained within the context of both Tsallis and Kaniadakis statistics. We have demonstrated in an exact way that the value of the LQG Immirzi parameter can also be calculated using Tsallis, Kaniadakis and incomplete formalisms showing different behaviors, which confirms the distinction property of the parameter.
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