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A Generalization of Independence and Multivariate Student’s t-distributions

  • Monta Sakamoto
  • Hiroshi Matsuzoe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)

Abstract

In anomalous statistical physics, deformed algebraic structures are important objects. Heavily tailed probability distributions, such as Student’s t-distributions, are characterized by deformed algebras. In addition, deformed algebras cause deformations of expectations and independences of random variables. Hence, a generalization of independence for multivariate Student’s t-distribution is studied in this paper. Even if two random variables which follow to univariate Student’s t-distributions are independent, the joint probability distribution of these two distributions is not a bivariate Student’s t-distribution. It is shown that a bivariate Student’s t-distribution is obtained from two univariate Student’s t-distributions under q-deformed independence.

Keywords

Deformed exponential family Deformed independence Statistical manifold Tsallis statistics Information geometry 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Engineering School of Information and Digital TechnologiesEfreiVillejuifFrance
  2. 2.Department of Computer Science and Engineering Graduate School of EngineeringNagoya Institute of TechnologyNagoyaJapan

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