Abstract
In this paper, we discuss a method based on wavelet analysis for the study of the q-index of the Gaussian distribution. We derive q-index from the scale index, iscale, using the expression; q≡1+2iscale where iscale is a wavelet based tool for measuring the degree of aperiodicity of a dynamical system in the range of 0≤iscale≤1. We show that this expression gives consistent results with the numerical approach of q-Gaussian distribution which determines the degree of non-extensivity of a dynamical system in the range of 1<q<3. We also suggest a new entropy calculation method based on the normalized inner scalogram for studying the chaotic characteristics of nonlinear dynamical systems.
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