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

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Scarfone A., Suyari H., Wada T.
Open Physics
|
2009
|
vol. 7
|
issue 3
414-420
EN
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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A mathematical structure for the generalization of conventional algebra

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Kaabouchi A., Nivanen L., Wang Q., Badiali J., Méhauté A.
Open Physics
|
2009
|
vol. 7
|
issue 3
549-554
EN
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate an algebra in which the conventional algebraic rules are generalized.
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