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Plot of probability density at scale parameter equal to 1

Class of non-Gaussian distributions with zero skewness and kurtosis

Aleksandr I. Krasil'nikov


A mathematical model of non-Gaussian distributions with zero skewness and kurtosis has been defined. This model represents a class of two-component mixtures of conjugate distributions with equal weight coefficients. An equation was obtained that the second and fourth initial moments of the mixture components should satisfy. Examples of non-Gaussian distributions with zero skewness and kurtosis were considered. These examples showed that the sixth and eighth cumulant coefficients in such distributions could be positive, negative or nonexistent. The obtained results make it possible to perform the mathematical and computer simulation of non-Gaussian distributions with zero skewness and kurtosis.


non-Gaussian distribution; coefficient of skewness; coefficient of kurtosis; mathematical simulation; computer simulation; random quantity; characteristic function; cumulant coefficient

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