A generalization of independence and multivariate Student's t-distributions

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14272

Résumé

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.

A generalization of independence and multivariate Student's t-distributions

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application/pdf A generalization of independence and multivariate Student's t-distributions Monta Sakamoto, Hiroshi Matsuzoe
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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.
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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.

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A generalization of independence and multivariate Student’s t-distributions MATSUZOE Hiroshi Nagoya Institute of Technology joint works with SAKAMOTO Monta (Efrei, Paris) 1 Deformed exponential family 2 Non-additive differentials and expectation functionals 3 Geometry of deformed exponential families 4 Generalization of independence 5 q-independence and Student’s t-distributions 6 Appendix   Notions of expectations, independence are determined from the choice of statistical models.  Introduction: Geometry and statistics • Geometry for the sample space • Geometry for the parameter space • Wasserstein geometry • Optimal transport theory • A pdf is regarded as a distribution of mass • Information geometry • Convexity of entropy and free energy • Duality of estimating function