GSI 2015: Geometric Science of Information pp 740-749

# 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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