New power-law tailed distributions emerging in $\kappa$-statistics

TL;DR

This paper introduces new power-law tailed distributions derived from $$-deformed exponential functions within $$-statistics, expanding the toolkit for modeling data with heavy tails.

Contribution

It presents novel classes of statistical distributions based on $$-deformed exponential functions, generalizing known distributions for data with power-law tails.

Findings

New $$-deformed distributions for Gamma, Weibull, Logistic models.

Distributions suitable for data with power-law tails.

Framework connects $$-statistics with heavy-tailed data analysis.

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's factor, emerges properly deformed within this formalism. Starting from this, so-called $\kappa$-deformed exponential function, we introduce new classes of statistical distributions emerging as the $\kappa$-deformed version of already known distribution as the Generalized Gamma, Weibull, Logistic which can be adopted in the analysis of statistical data that exhibit power-law tails.