Geodesic
The generalization of the hyperbolic secant distribution and the logistic distribution in the single dostribution with variable kurtosis
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 74-81 
E. V. Kaplya. The generalization of the hyperbolic secant distribution and the logistic distribution in the single dostribution with variable kurtosis. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 74-81. http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a7/
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     title = {The generalization of the hyperbolic secant distribution and the logistic distribution in the single dostribution with variable kurtosis},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] N. Balakrishnan, Handbook of the logistic distribution, Marcel Dekker, New York, 1992 | MR | Zbl

[2] N. Balakrishnan and V. B. Nevzorov, A primer on statistical distributions, John Wiley Sons, Inc., Hoboken, New Jersey, 2003 | MR

[3] N. L. Johnson, S. Kotz, N. Balakrishnan, Continuous univariate distributions, 2-nd edition, v. 2, John Wiley Sons, Inc., Hoboken, 1995 | MR

[4] E. V. Kaplya, “Obobschenie logisticheskogo zakona raspredeleniya v statisticheskom analize dinamiki napravleniya vetra”, Izvestiya RAN. Fizika atmosfery i okeana, 52:6 (2016), 669–675 | DOI

[5] E. V. Kaplya, “Obobschenie logisticheskogo zakona raspredeleniya v modeli dinamiki napravleniya vetra”, Geofizicheskie protsessy i biosfera, 14:4 (2015), 61–71

[6] P. Ding, “Three occurrences of the hyperbolic-secant distribution”, The American Statistician, 68 (2014), 32–335 | DOI | MR

[7] B. Ramachandran, Teoriya kharakteristicheskikh funktsii, Nauka, M., 1975

[8] G. Casella and R. Berger, Statistical inference, 2-nd edition, Wadsworth Group, Duxbury, 2002 | MR

[9] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark, NIST handbook of mathematical functions, U.S. Department of Commerce, Cambridge University Press., 2010, National Institute of Standards and Technology (NIST) | MR

[10] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs and mathematical tables, 10th ed., Dover, New York, 1972 | MR

[11] S. A. Aivazyan, I. S. Enyukov, L. D. Meshalkin, Prikladnaya statistika: Osnovy modelirovaniya i pervichnaya obrabotka dannykh, Spravochnoe izd., Finansy i statistika, M., 1983 | MR