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The generalization of the hyperbolic secant distribution and the logistic distribution in the single dostribution with variable kurtosis

E. V. Kaplya

Volzhsk Branch of Moscow Power Engineering Institute

Abstract: The generalization V of the logistic distribution is proposed and investigated. For a random variable having a generalized logistic distribution of type V, the characteristic function is found, the generating function of moments is formed, and the expression of dispersion is obtained. The dependence of the kurtosis coefficient of the generalized logistic distribution on the power parameter is found and investigated. The interval of values of the coefficient of kurtosis of the generalized logistic distribution is determined. It is found that the coefficient of kurtosis depends only on the power parameter.

Key words: logistic distribution, hyperbolic secant, probability density, characteristic function of the random variable, moment-generating function, excess kurtosis, probability distribution function.

UDC: 519.213.7

MSC: 11K06

Received: 30.10.2019

DOI: 10.47910/FEMJ202008