Riemann-Finsler geometry with applications to information geometry

Chinese Annals of Mathematics. Series B

Volumn 27, Issue 1, 2006, Pages 73-94

  Shen, Zhongmin ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Information geometry; Riemann Finsler geometry

Indexed keywords

EID: 33747881005     PISSN: 02529599     EISSN: 18606261     Source Type: Journal    
DOI: 10.1007/s11401-005-0333-3     Document Type: Article

References (13)

1. Amari, S.-I. and Nagaoka, H., Methods of Information Geometry, Oxford University Press and Amer. Math. Soc., 2000.
2. Bao, D., Chern, S. S. and Shen, Z., An Introduction to Riemann-Finsler Geometry, Springer, 2000.
3. Amari, S.-I., Differential Geometrical Methods in Statistics, Springer Lecture Notes in Statistics, 20, Springer, 2002.
4. Dodson, C. T. J. and Matsuzoe, H., An affine embedding of the gamma manifold, Appl. Sci. (electronic), 5(1), 2003, 7-12.
5. Dzhafarov, E. D. and Colonius, H., Fechnerian metrics in unidimensional and multidimensional stimulus, Psychological Bulletin and Review, 6, 1999, 239-268.
6. Dzhafarov, E. D. and Colonius, H., Fechnerian scaling, probability-distance hypothesis, and Thurstonian link, Technical Report #45, Purdue Mathematical Psychology Program.
7. Dzhafarov, E. D. and Colonius, H., Fechnerian Metrics, Looking Back: The End of the 20th Century Psychophysics, P. R. Kileen & W. R. Uttal (eds.), Arizona University Press, Tempe, AZ, 111-116.
8. Hwang, T.-Y. and Hu, C.-Y., On a characterization of the gamma distribution: The independence of the sample mean and the sample coefficient of variation, Annals Inst. Statist. Math., 51, 1999, 749-753.
9. Lauritzen, S. L., Statistical manifolds, Differential Geometry in Statistical Inferences, IMS Lecture Notes Monograph Series, 10, Hayward California, 1987, 96-163.
10. Murray, M. K. and Rice, J. W., Differential Geometry and Statistics, Chapman & Hall, London, 1995.
11. Nagaoka, H. and Amari, S., Differential geometry of smooth families of probability distributions, Univ. Tokyo, Tokyo, Japan, METR, 82-7, 1982.
12. Shen, Z., Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
13. Shen, Z. and Yildirim, G. C., A characterization of Funk metrics, preprint, 2005.