Article,
Creating kappa-like distributions from a Galton board
Physica A: Statistical Mechanics and its Applications, 390 (7): 1248 - 1257 (2011)
DOI: http://dx.doi.org/10.1016/j.physa.2010.11.044
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.
