Classification of Models of Two-component Mixtures of Symmetrical Distributions with Zero Kurtosis Coefficient

Abstract

On the basis of a family of two-component mixtures of distributions, a class K of symmetric non-Gaussian distributions with a zero kurtosis coefficient is defined, which is divided into two groups and five types. The dependence of the fourth-order cumulant on the weight coefficient of the mixture is studied, as a result of which the conditions are determined under which the kurtosis coefficient of the mixture is equal to zero. The use of a two-component mixture of Subbotin distributions for modeling single-vertex symmetric distributions with a zero kurtosis coefficient is justified. Examples of symmetric non-Gaussian distributions with zero kurtosis coefficient are given. The use of class K models gives a practical opportunity at the design stage to compare the effectiveness of the developed methods and systems for non-Gaussian signals with zero coefficients of asymmetry and kurtosis processing.