$κ$-generalization of Gauss' law of error

Abstract

Based on the $κ$-deformed functions ($κ$-exponential and $κ$-logarithm) and associated multiplication operation ($κ$-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 $κ$-product. This $κ$-generalized maximum likelihood principle leads to the {\it so-called} $κ$-Gaussian distributions.