Аналіз коефіцієнта ексцесу двокомпонентних сумішей зсунутих негаусових розподілів

Abstract

The dependence of the extremes and zeros of the excess kurtosis on the weight coefficient 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 under which the extrema points belong to the interval 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 are real and belong to the interval 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.