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How Should the Distance of Probability Assignments Be Judged?

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Abstract

It is shown that the l 1-distance in the space of probability assignments on a finite set Ω provides a criterion to judge whether two assignments are too close to each other to be distinguished by a statistical test. The criterion is independent of the number of elements of Ω. Other notions of distance are also discussed.

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References

  1. Abe, S.: Phys. Rev. E 66, 046134 (2002)

    Article  ADS  Google Scholar 

  2. Souza, A.M.C., Tsallis, C.: Phys. Lett. A 319, 273 (2003)

    Article  MATH  ADS  Google Scholar 

  3. Lesche, B.: Phys. Rev. E 70, 017102 (2004)

    Article  ADS  Google Scholar 

  4. Naudts, J.: Rev. Math. Phys. 16, 809 (2004)

    Article  MATH  Google Scholar 

  5. Curado, E.M.F., Nobre, F.D.: Phys. A 335, 94 (2004)

    Google Scholar 

  6. Kaniadakis, G., Scarfone, A.M.: Phys. A 340, 102 (2004)

    Google Scholar 

  7. Abe, A., Kaniadakis, G., Scarfone, A.M.: J. Phys. A: Math. Gen. 37, 10513 (2004)

    Article  MATH  ADS  Google Scholar 

  8. Abe, S.: Phys. Rev. E 72, 028102 (2005)

    Article  ADS  Google Scholar 

  9. Ruch, E.: Theor. Chim. Acta 38, 167 (1975)

    Article  Google Scholar 

  10. Lesche, B.: J. Stat. Phys. 27, 419 (1982)

    Article  Google Scholar 

  11. Reif, F.: Fundamentals of Statistical and Thermal Physics. McGraw–Hill, New York (1965)

    Google Scholar 

  12. Lindgren, B.W.: Statistical Theory, 4th edn. Chapman & Hall, New York (1993)

    MATH  Google Scholar 

  13. Csiszár, I.: Stud. Sci. Math. Hung. 2, 299 (1967)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Physics, University of Tsukuba, Ibaraki, 305-8571, Japan

    Sumiyoshi Abe

  2. Departamento de Física, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, 360 36 900, Brazil

    Bernhard Lesche & Jens Mund

Authors
  1. Sumiyoshi Abe
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  2. Bernhard Lesche
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  3. Jens Mund
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Correspondence to Bernhard Lesche.

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Abe, S., Lesche, B. & Mund, J. How Should the Distance of Probability Assignments Be Judged?. J Stat Phys 128, 1189–1196 (2007). https://doi.org/10.1007/s10955-007-9344-7

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  • DOI: https://doi.org/10.1007/s10955-007-9344-7

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