A generalization of independence and multivariate Student's t-distributions - Hiroshi Matsuzoe, Monta Sakamoto
Authors : Hiroshi Matsuzoe, Monta Sakamoto
DOI URL : http://dx.doi.org/10.1007/978-3-319-25040-3_79
Video : http://www.youtube.com/watch?v=hGc1z8EYR24
Slides: Matsuzoe-generalization independence Student.pdf
Presentation : https://www.see.asso.fr/node/14272
Creative Commons Attribution-ShareAlike 4.0 International
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.