Far Eastern Mathematical Journal

To content of the issue


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


Kaplya E.V.

2020, issue 1, Ñ. 74–81
DOI: https://doi.org/10.47910/FEMJ202008


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.

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

Download the article (PDF-file)

References

[1] N. Balakrishnan, Handbook of the logistic distribution, Marcel Dekker, New York, 1992.
[2] N. Balakrishnan and V. B. Nevzorov, A primer on statistical distributions, John Wiley & Sons, Inc., Hoboken, New Jersey, 2003.
[3] N. L. Johnson, S. Kotz, N. Balakrishnan, Continuous univariate distributions, 2-nd edition, v. 2, John Wiley & Sons, Inc., Hoboken, 1995.
[4] E.V. Kaplia, “ Obobshchenie logisticheskogo zakona raspredeleniia v statisticheskom ana- lize dinamiki napravleniia vetra” , Izvestiia RAN. Fizika atmosfery i okeana, 52:6, (2016), 669–675.
[5] E. V. Kaplia, “Obobshchenie logisticheskogo zakona raspredeleniia v modeli dinamiki napravleniia vetra” , Geofizicheskie protsessy i biosfera, 14:4, (2015), 61–71.
[6] P. Ding, “Three occurrences of the hyperbolic-secant distribution”, The American Statisti- cian, 68, (2014), 32–335.
[7] B. Ramachandran, Teoriia kharakteristicheskikh funktsii, Nauka, M., 1975.
[8] G. Casella and R. Berger, Statistical inference, 2-nd edition, Wadsworth Group, Duxbury, 2002.
[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., National Institute of Standards and Technology (NIST), 2010.
[10] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs and mathematical tables, 10th ed., Dover, New York, 1972.
[11] S.A. Aivazian, I. S. Eniukov, L. D. Meshalkin, Prikladnaia statistika: Osnovy mo- delirovaniia i pervichnaia obrabotka dannykh, Spravochnoe izd., Finansy i statistika, M., 1983.

To content of the issue