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For two-component mixtures of shifted distributions a general formula for finding the value of the shift parameter ã0,s, at which the cumulant coefficients γs ( p ã) of any order s ≥ 3 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 γ6 ( p, ã) 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. [ABSTRACT FROM AUTHOR]

The dependence of the extremes and zeros of the excess kurtosis γ4(p, ã ) on the weight coefficient P is researched. Formulas for finding the extrema points, the values of the minimums and maximums of the excess kurtosis are obtained. Conditions on the shift parameter ã under which the extrema points belong to the interval [0;1] are determined. Formulas for finding the zeros of the excess kurtosis are obtained and conditions on shift parameter under which the roots of the equation γ4(p, ã ) are real and belong to the interval [0;1] are determined. Examples of calculating extremes and zeros of the excess kurtosis of two-component mixtures of shifted non-Gaussian distributions are considered. The results of the research justify the possibility of practical application of two-component mixtures of shifted distributions for mathematical and computer modeling of an infinite number of non-Gaussian random variables with negative, positive and zero excess kurtosis. [ABSTRACT FROM AUTHOR]

The dependence of the cumulant coefficients of two-component mixtures of shifted nonGaussian 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. [ABSTRACT FROM AUTHOR]