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  4. 2024
  5. VOL 46, NO 4 (2024)
  6. pp. 19-38

MODELING OF TWO-COMPONENT MIXTURES OF SHIFTED DISTRIBUTIONS WITH ZERO CUMULANT COEFFICIENTS

A.I. Krasilnikov

Èlektron. model. 2024, 46(4):19-38

https://doi.org/10.15407/emodel.46.04.019

ABSTRACT

For two-component mixtures of shifted distributions a general formula for finding the value of the shift parameter , at which the cumulant coefficients  of any order are equal to zero, is obtained. An algorithm for mathematical and computer modeling of two-component mixtures of shifted distributions with zero cumulant coefficients is formulated. General formulas for two-component mixtures of shifted gamma-distributions with zero cumulant coefficients of any order are obtained and examples of mixtures with zero skewness and kurtosis coefficients are given. General formulas of two-component mixtures of shifted Student’s distributions with zero cumulant coefficients of any order are obtained and examples of mixtures with zero kurtosis coefficient and coefficient  are given. The research results provide the practical possibility of using two-component mixtures of shifted distributions for mathematical and computer modeling of non-Gaussian random variables with zero cumulant coefficients of any order.

KEYWORDS

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

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