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Generalized log-likelihood functions and Bregman divergences

J. Math. Phys. 50, 113301 (2009); doi:10.1063/1.3257917

Published 10 November 2009

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Tatsuaki Wada
Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511, Japan
Based on a two-parameter generalization of Gauss' law of error, a generalized log-likelihood is related to a Bregman divergence. This relation is a two-parameter generalization of the well-known relation between log-likelihood and Kullback–Leibler divergence. ©2009 American Institute of Physics
History: Received 4 December 2008; accepted 8 October 2009; published 10 November 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/113301/1
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KEYWORDS and PACS

Keywords
PACS
  • 02.50.Cw
    Probability theory
  • YEAR: 2009

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0022-2488 (print)   1089-7658 (online)
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REFERENCES (18)

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  1. R. A. Fisher, Statistical Methods for Research Workers (Oliver and Boyd, Edinburgh, 1925).
  2. S. Kullback, Information Theory and Statistics (Wiley, New York, 1959).
  3. I. Csiszár, Stud. Sci. Math. Hung. 2, 229 (1967).
  4. J. Naudts, Rev. Math. Phys. 16, 809 (2004)
  5. J. Naudts and J. Ineq, Pure Appl. Math. 5, 1 (2004).
  6. F. Topsøe, AIP Conf. Proc. 965, 104 (2007).
  7. L. M. Bregman, USSR Comput. Math. Math. Phys. 7, 200 (1967).
  8. D. Petz, Acta Math. Hungar. 116, 127 (2007).
  9. C. F. Gauß, Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium (F. Perthes and I. H. Besser, Hamburg, 1809).
  10. E. T. Jaynes, Probability Theory: The Logic of Science, edited by G. L. Bretthorst (Cambridge University Press, Cambridge, 2003).
  11. B. H. Lavenda, Statistical Physics: A Probabilistic Approach (Wiley, New York, 1991).
  12. H. Suyari and M. Tsukada, IEEE Trans. Inf. Theory 51, 753 (2005).
  13. T. Wada and H. Suyari, Phys. Lett. A 348, 89 (2006).
  14. G. Kaniadakis, M. Lissia, and A. M. Scarfone, Physica A 340, 41 (2004).
  15. B. D. Sharma and L. J. Taneja, Metrika 22, 205 (1975)
  16. D. P. Mittal, ibid. 22, 35 (1975).
  17. A. M. Scarfone, H. Suyari, and T. Wada, Cent. Eur. J. Phys. 7, 414 (2009).
  18. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
  19. G. Kaniadakis, Physica A 296, 405 (2001).
  20. T. Wada and H. Suyari, Phys. Lett. A 368, 199 (2007).

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