Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

Antonio Scarfone 1 , Hiroki Suyari 2 , and Tatsuaki Wada 3
  • 1 Dipartimento di Fisica Politecnico di Torino, Istituto Nazionale per la Fisica della Materia (CNR-INFM), I-10129, Torino, Italy
  • 2 Graduate School of Advanced Integration Science, Chiba University, 263-8522, Chiba, Japan
  • 3 Department of Electrical and Electronic Engineering, Ibaraki University, 316-8511, Hitachi, Japan

Abstract

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.

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