Kaniadakis Distribution Physically Closer to a Maxwell-Boltzmann at Low e Than the Tsallis?

The Kaniadakis and Tsallis distributions both have the property that in the large e/T limit, they drop as power laws, i.e. (ke/T) power 1/k and (1-q) e/T power 1/(1-q). If 1-q = k, then this is the same power law. Mathematically, both distributions are presented as transforming into the Maxwell-Boltzmann distribution for k=0, or q=1. The question we ask is: If physically one is interested in the power law drop-off for e/T>>1 which is associated with a finite k and a q not=1, then why would one be at all interested whether the distributions transformed to Maxwell-Boltzmann ones in the k=0 or q=1 limit? We try to analyze the situation in the following manner. A finite k or q not=1 are the physical values of interest, not k=0 or q=1. This being said, the distribution should not be 0 for e/T