New power-law tailed distributions emerging in κ-statistics

Over the last two decades, it has been argued that the Lorentz transformation mechanism, which imposes the generalization of Newton's classical mechanics into Einstein's special relativity, implies a generalization, or deformation, of the ordinary statistical mechanics. The exponential function, which defines the Boltzmann factor, emerges properly deformed within this formalism. Starting from this, the so-called kappa-deformed exponential function, we introduce new classes of statistical distributions emerging as the kappa-deformed versions of already known distribution as the Generalized Gamma, Weibull, Logistic ones which can be adopted in the analysis of statistical data that exhibit power-law tails. Copyright (c) 2021 EPLA

Automated summary

Studies have shown that the Lorentz transformation mechanism may lead to a generalization or deformation of ordinary statistical mechanics, with the exponential function properly deformed in this formalism. By introducing the kappa-deformed exponential function, new classes of statistical distributions can be generated for analyzing statistical data with power-law tails.