$\kappa$-generalization of Gauss' law of error

TL;DR

This paper introduces a new one-parameter generalization of Gauss' law of error using Kaniadakis' $$-deformed functions, resulting in $$-Gaussian distributions through a $$-generalized maximum likelihood approach.

Contribution

It develops a novel $$-generalization of Gauss' law of error based on $$-deformed functions, expanding the framework of error distribution models.

Findings

Derivation of $$-Gaussian distributions from the generalized likelihood.

Extension of Gauss' law of error using $$-deformed algebra.

Introduction of a $$-generalized maximum likelihood principle.

Abstract

Based on the $\kappa$-deformed functions ($\kappa$-exponential and $\kappa$-logarithm) and associated multiplication operation ($\kappa$-product) introduced by Kaniadakis (Phys. Rev. E \textbf{66} (2002) 056125), we present another one-parameter generalization of Gauss' law of error. The likelihood function in Gauss' law of error is generalized by means of the $\kappa$-product. This $\kappa$-generalized maximum likelihood principle leads to the {\it so-called} $\kappa$-Gaussian distributions.