Abstract: A divergence function is a skew-symmetric distance like function on a manifold. In the geometric theory of statistical inference, such a divergence function is useful. In complex systems, Tsallis anomalous statistics is developing rapidly. A q-exponential family is an important statistical model in Tsallis statistics. For this q-exponential family, a divergence function is constructed from the viewpoint of affine differential geometry.

Keywords: information geometry, affine differential geometry, Tsallis statistics, divergence, q-exponential family

ACM Classification Keywords: G.0 General

MSC: 53A15, 62B10, 53A30

Link:

CONSTRUCTION OF GEOMETRIC DIVERGENCE ON q-EXPONENTIAL FAMILY

Hiroshi Matsuzoe

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p08.pdf