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  5. VOL 47, NO 4 (2025)
  6. pp. 21-38

Class of Two-component Mixtures of Non-gaussian Symmetric Distributions with Zero Cumulant Coefficients

A.I. Krasilnikov

Èlektron. model. 2025, 47(4):21-38

https://doi.org/10.15407/emodel.47.04.021

ABSTRACT

Based on a family of two-component mixtures of distributions, a class К of symmetric non-Gaussian distributions with zero cumulant coefficients s of order is defined. Formulas for finding the values of the mixture’s weight coefficient, at which the coefficients 4, 6 are equal to zero, are obtained. The dependence of the cumulant coefficient on the mixture’s weight coefficient 8 is researched, as a result of which the conditions, under which the mixtu­re’s coefficient 8 is equal to zero, is determined. Formulas for finding of the mixture’s weight coefficient values, at which the coefficient 8 = 0, are obtained. Examples of symmetric non-Gaussian distributions with zero cumulant coefficients 4, 6, 8 are considered. A methodology for computer modeling of non-Gaussian random variables of the class К is given.

KEYWORDS

non-Gaussian symmetric distributions, two-component mixtures of distributions, cumulant coefficients, kurtosis coefficient.

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