A generalization of independence and multivariate Student's tdistributions  Hiroshi Matsuzoe, Monta Sakamoto

Authors : Hiroshi Matsuzoe, Monta Sakamoto
DOI URL : http://dx.doi.org/10.1007/9783319250403_79
Video : http://www.youtube.com/watch?v=hGc1z8EYR24
Slides: Matsuzoegeneralization independence Student.pdf
Presentation : https://www.see.asso.fr/node/14272
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
In anomalous statistical physics, deformed algebraic structures are important objects. Heavily tailed probability distributions, such as Student’s tdistributions, 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 tdistribution is studied in this paper. Even if two random variables which follow to univariate Student’s tdistributions are independent, the joint probability distribution of these two distributions is not a bivariate Student’s tdistribution. It is shown that a bivariate Student’s tdistribution is obtained from two univariate Student’s tdistributions under qdeformed independence.