Creating kappa-like distributions from a Galton board

M. Leitner, M.P. Leubner and Z. Vörös

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 7, 1248-1257

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.

Keywords: Galton board; Nonextensive statistics; Kappa distributions; 2-D Lorentz gas (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:7:p:1248-1257

DOI: 10.1016/j.physa.2010.11.044

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