New power-law tailed distributions emerging in κ-statistics (a)

Abstract

Abstract 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 κ-deformed exponential function, we introduce new classes of statistical distributions emerging as the κ-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.