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Student's t- and r-distributions: Unified derivation from an entropic variational principle

Author

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  • de Souza, AndréM.C.
  • Tsallis, Constantino

Abstract

The optimization of the recently generalized entropy of the form Sq ≡ 1 − ∝dx[p(x)]q∼/(q−1) with the constraints ∝dxp(x) = 1 and 〈x2〉q ≡ ∝dxx2[p(x)]q = 1 yields the Student's t-distribution for q > 1, and the r-distribution for q < 1.

Suggested Citation

  • de Souza, AndréM.C. & Tsallis, Constantino, 1997. "Student's t- and r-distributions: Unified derivation from an entropic variational principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 236(1), pages 52-57.
    • Handle: RePEc:eee:phsmap:v:236:y:1997:i:1:p:52-57
    DOI: 10.1016/S0378-4371(96)00395-0
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    Cited by:

    1. Nelson, Kenric P. & Umarov, Sabir R. & Kon, Mark A., 2017. "On the average uncertainty for systems with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 30-43.
    2. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    3. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    4. Nadarajah, Saralees & Kotz, Samuel, 2007. "On the q-type distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 465-468.
    5. Cirto, Leonardo J.L. & Assis, Vladimir R.V. & Tsallis, Constantino, 2014. "Influence of the interaction range on the thermostatistics of a classical many-body system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 286-296.
    6. Tsallis, Constantino & Borges, Ernesto P., 2021. "Comment on “Pricing of financial derivatives based on the Tsallis statistical theory” by Zhao, Pan, Yue and Zhang," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    7. Zhenpeng Li & Xijin Tang & Zhenjie Hong, 2022. "Collective attention dynamic induced by novelty decay," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-11, August.
    8. Jose, K.K. & Naik, Shanoja R., 2008. "A class of asymmetric pathway distributions and an entropy interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(28), pages 6943-6951.

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