κ-generalization of Gauss' law of error

Based on the κ-deformed functions (κ-exponential and κ-logarithm) and associated multiplication operation (κ-product) introduced by Kaniadakis [Phys. Rev. E 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 so-called κ-Gaussian distributions.