# ANALYSIS OF CUMULANT COEFFICIENTS OF TWO-COMPONENT MIXTURES OF SHIFTED NON-GAUSSIAN DISTRIBUTIONS

A.I. Krasilnikov

Èlektron. model. 2021, 43(5):73-92
https://doi.org/10.15407/emodel.43.05.073

### ABSTRACT

The dependence of the cumulant coefficients of two-component mixtures of shifted non-Gaussian distributions on the weight coefficient is analyzed and conditions are determined under which the cumulant coefficients of any orders are equal to zero. The dependence of the cumulant coefficients of two-component mixtures on the shear parameter is investigated and the parameter values are determined at which the cumulant coefficients of any orders have ext­rema and zeros. The dependence of the skewness and excess kurtosis of a two-component mixture of shifted Gumbel distributions of type 1 on the weight coefficient and the shear parameter is investigated and their values are obtained at which the skewness and excess kurtosis of the mixture are equal to zero. The features of computer modeling of random variables, the probability density of which is a two-component mixture of shifted distributions, are considered.

### KEYWORDS

non-Gaussian distributions, two-component mixtures of distributions, cumulant analysis, cumulant coefficients, asymmetry coefficient, excess coefficient.

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