Study of the q-Gaussian distribution with the scale index and calculating entropy by normalized inner scalogram

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, i(scale). using the expression; q Xi 1 + 2i(scale) where i scale is a wavelet based tool for measuring the degree of aperiodicity of a dynamical system in the range of O <= i(scale) <= 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.