Next Article in Journal
Recent Theoretical Approaches to Minimal Artificial Cells
Next Article in Special Issue
Information Geometric Complexity of a Trivariate Gaussian Statistical Model
Previous Article in Journal / Special Issue
Computational Information Geometry in Statistics: Theory and Practice
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(5), 2472-2487; doi:10.3390/e16052472

F-Geometry and Amari’s α-Geometry on a Statistical Manifold

Indian Institute of Space Science and Technology, Department of Space, Government of India, Valiamala P.O, Thiruvananthapuram-695547, Kerala, India
Authors to whom correspondence should be addressed.
Received: 13 December 2013 / Revised: 21 April 2014 / Accepted: 25 April 2014 / Published: 6 May 2014
(This article belongs to the Special Issue Information Geometry)
View Full-Text   |   Download PDF [220 KB, uploaded 24 February 2015]   |  


In this paper, we introduce a geometry called F-geometry on a statistical manifold S using an embedding F of S into the space RX of random variables. Amari’s α-geometry is a special case of F-geometry. Then using the embedding F and a positive smooth function G, we introduce (F,G)-metric and (F,G)-connections that enable one to consider weighted Fisher information metric and weighted connections. The necessary and sufficient condition for two (F,G)-connections to be dual with respect to the (F,G)-metric is obtained. Then we show that Amari’s 0-connection is the only self dual F-connection with respect to the Fisher information metric. Invariance properties of the geometric structures are discussed, which proved that Amari’s α-connections are the only F-connections that are invariant under smooth one-to-one transformations of the random variables. View Full-Text
Keywords: embedding; Amari’s α-connections; F-metric; F-connections; (F,G)-metric; (F,G)-connections; invariance embedding; Amari’s α-connections; F-metric; F-connections; (F,G)-metric; (F,G)-connections; invariance

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

V., H.K.; S., S.M.K. F-Geometry and Amari’s α-Geometry on a Statistical Manifold. Entropy 2014, 16, 2472-2487.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top