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Creating kappa-like distributions from a Galton board

Author

Listed:
  • Leitner, M.
  • Leubner, M.P.
  • Vörös, Z.

Abstract

The Galton board is a classical device demonstrating geometrically the formation of normal distributions. In view of long-range interactions, governed by nonextensive statistics, the concept of the Galton board is extended providing numerically the corresponding power-law distributions. Within nonextensive statistics kappa-distributions, which are linked to q-Gaussians, are a consequence from entropy generalization. In this way the transition from normal distributions to kappa-like distributions (where kappa is the entropic index) is available within a Galton board concept where both the generalized distributions for positive and negative kappa-like values are reproduced. Based on two similar numerical approaches it is shown how positive kappa-like exponents are related to memory effects and negative kappa-like exponents to enhanced interactions of increased order in the system, as compared to the normal distribution case.

Suggested Citation

  • Leitner, M. & Leubner, M.P. & Vörös, Z., 2011. "Creating kappa-like distributions from a Galton board," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1248-1257.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:7:p:1248-1257
    DOI: 10.1016/j.physa.2010.11.044
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    References listed on IDEAS

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    1. Benito, J.G. & Ippolito, I. & Vidales, A.M., 2008. "Improving mixture of grains by using bi-dimensional Galton boards," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5371-5380.
    2. A. D. Chepelianskii, 2006. "Microwave control of directed transport in asymmetric antidot structures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 52(3), pages 389-396, August.
    3. R. Hanel & S. Thurner & C. Tsallis, 2009. "Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(2), pages 263-268, November.
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