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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 25, 2009

Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

  • Antonio Scarfone EMAIL logo , Hiroki Suyari and Tatsuaki Wada
From the journal Open Physics

Abstract

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.

[1] A. M. Scarfone, P. Quarati, G. Mezzorani, M. Lissia, Astrophys. Space Sci. 315, 353 (2008) http://dx.doi.org/10.1007/s10509-008-9842-310.1007/s10509-008-9842-3Search in Google Scholar

[2] A. Ohara, T. Wada, arXiv:0810.0624v1 Search in Google Scholar

[3] M. Gell-Mann, C. Tsallis, Nonextensive entropy (Oxford University Press, New York, 2004) 10.1093/oso/9780195159769.001.0001Search in Google Scholar

[4] C. F. Gauss, Theoria motus corporum coelestium in sectionibus conicis solem ambientum (Hamburg, F. Perthes and I. H. Besser, 1809) Search in Google Scholar

[5] C. Tsallis, S. M. Duarte Querio, AIP Conf. Proc. 965, 8 (2007) http://dx.doi.org/10.1063/1.282876510.1063/1.2828765Search in Google Scholar

[6] L. G. Moyano, C. Tsallis, M. Gell-Mann, Europhys. Lett. 73, 813 (2006) http://dx.doi.org/10.1209/epl/i2005-10487-110.1209/epl/i2005-10487-1Search in Google Scholar

[7] B. D. Sharma, I. J. Taneja, Metrika 22, 205 (1975) http://dx.doi.org/10.1007/BF0189972810.1007/BF01899728Search in Google Scholar

[8] D. P. Mittal, Metrika 22, 35 (1975) http://dx.doi.org/10.1007/BF0189971210.1007/BF01899712Search in Google Scholar

[9] G. Kaniadakis, A. M. Scarfone, Physica A 305, 69 (2002) http://dx.doi.org/10.1016/S0378-4371(01)00642-210.1016/S0378-4371(01)00642-2Search in Google Scholar

[10] E. P. Borges, Physica A 340, 95 (2004) http://dx.doi.org/10.1016/j.physa.2004.03.08210.1016/j.physa.2004.03.082Search in Google Scholar

[11] L. Nivanen, A. Le Méhauté, Q. A. Wang, Rep. Math. Phys. 52, 437 (2003) http://dx.doi.org/10.1016/S0034-4877(03)80040-X10.1016/S0034-4877(03)80040-XSearch in Google Scholar

[12] C. Tsallis, M. Gell-Mann, Y. Sato, P. Natl. Acad. Sci. USA 102, 15377 (2005) http://dx.doi.org/10.1073/pnas.050380710210.1073/pnas.0503807102Search in Google Scholar PubMed PubMed Central

[13] H. Suyari, T. Wada, Physica A 387, 71 (2008) http://dx.doi.org/10.1016/j.physa.2007.07.07410.1016/j.physa.2007.07.074Search in Google Scholar

[14] H. Suyari, Physica A 368, 63 (2006) http://dx.doi.org/10.1016/j.physa.2005.12.06110.1016/j.physa.2005.12.061Search in Google Scholar

[15] H. Suyari, M. Tsukada, IEEE T. Inform. Theory 51, 753 (2005) http://dx.doi.org/10.1109/TIT.2004.84086210.1109/TIT.2004.840862Search in Google Scholar

[16] T. Wada, H. Suyari, Phys. Lett. A 348, 89 (2006) http://dx.doi.org/10.1016/j.physleta.2005.08.08610.1016/j.physleta.2005.08.086Search in Google Scholar

[17] G. Kaniadakis, M. Lissia, A. M. Scarfone, Phys. Rev. E 71, 046128 (2005) http://dx.doi.org/10.1103/PhysRevE.71.04612810.1103/PhysRevE.71.046128Search in Google Scholar PubMed

[18] G. Kaniadakis, M. Lissia, A. M. Scarfone, Physica A 340, 41 (2004) http://dx.doi.org/10.1016/j.physa.2004.03.07510.1016/j.physa.2004.03.075Search in Google Scholar

[19] S. Abe, G. Kaniadakis, A. M. Scarfone, J. Phys. AMath. Gen. 37, 10513 (2004) http://dx.doi.org/10.1088/0305-4470/37/44/00410.1088/0305-4470/37/44/004Search in Google Scholar

[20] R. Tonelli, G. Mezzorani, F. Melloni, M. Lissia, M. Coraddu, Prog. Theor. Phys. 115, 23 (2006) http://dx.doi.org/10.1143/PTP.115.2310.1143/PTP.115.23Search in Google Scholar

[21] T. Wada, H. Suyari, Phys. Lett. A 368, 199 (2007) http://dx.doi.org/10.1016/j.physleta.2007.04.00910.1016/j.physleta.2007.04.009Search in Google Scholar

[22] A. M. Scarfone, Physica A 365, 63 (2006) http://dx.doi.org/10.1016/j.physa.2006.01.02310.1016/j.physa.2006.01.023Search in Google Scholar

[23] A. M. Scarfone, T. Wada, Phys. Rev. E 72, 026123 (2005) http://dx.doi.org/10.1103/PhysRevE.72.02612310.1103/PhysRevE.72.026123Search in Google Scholar

[24] C. Tsallis, J. Stat. Phys. 52, 479 (1988) http://dx.doi.org/10.1007/BF0101642910.1007/BF01016429Search in Google Scholar

[25] G. Kaniadakis, Phys. Rev. E 66, 056125 (2002) http://dx.doi.org/10.1103/PhysRevE.66.05612510.1103/PhysRevE.66.056125Search in Google Scholar

[26] S. Abe, Phys. Lett. A 224, 326 (1997) http://dx.doi.org/10.1016/S0375-9601(96)00832-810.1016/S0375-9601(96)00832-8Search in Google Scholar

Published Online: 2009-6-25
Published in Print: 2009-9-1

© 2009 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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