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Abstrakty
A generalized form of the usual Lognormal distribution, denoted with $𝓛𝓝_γ$, is introduced through the γ-order Normal distribution $𝓝_γ$, with its p.d.f. defined into (0,+∞). The study of the c.d.f. of $𝓛𝓝_γ$ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
99-110
Opis fizyczny
Daty
wydano
2013
otrzymano
2013-04-08
poprawiono
2013-09-11
Twórcy
autor
- Technological Educational Institute of Athens, 12210 Egaleo, Athens, Greece
Bibliografia
- [1] H. Alzer, On some inequalities for the incomplete gamma function, Mathematics of Computation 66 (1997) 771-778. doi: 10.1090/S0025-5718-97-00814-4.
- [2] F. Bernardeau and L. Kofman, Properties of the cosmological density distribution function, Monthly Notices of the Royal Astrophys. J. 443 (1995) 479-498.
- [3] P. Blasi, S. Burles and A.V. Olinto, Cosmological magnetic field limits in an inhomogeneous Universe, The Astrophysical Journal Letters 514 (1999) L79-L82. doi: 10.1086/311958.
- [4] E.L. Crow and K. Shimizu, Lognormal Distributions - Theory and Applications (M. Dekker, New York & Basel, 1998).
- [5] J. Gathen and J. Gerhard, Modern Computer Algebra (Cambridge University Press, 1993).
- [6] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Elsevier, 2007).
- [7] C.P. Kitsos and N.K. Tavoularis, Logarithmic Sobolev inequalities for information measures, IEEE Trans. Inform. Theory 55 (2009) 2554-2561. doi: 10.1109/TIT.2009.2018179.
- [8] C.P. Kitsos and T.L. Toulias, New information measures for the generalized normal distribution, Information 1 (2010) 13-27. doi: 10.3390/info1010013.
- [9] C.P. Kitsos, T.L. Toulias and C.P. Trandafir, On the multivariate γ-ordered normal distribution, Far East J. of Theoretical Statistics 38 (2012) 49-73.
- [10] T.J. Kozubowski and K. Podgórski, Asymmetric Laplace laws and modeling financial data, Math. Comput. Modelling 34 (2001) 1003-1021. doi: 10.1016/S0895-7177(01)00114-5.
- [11] T.J. Kozubowski and K. Podgórski, Asymmetric Laplace distributions, Math. Sci. 25 (2000) 37-46.
- [12] C.G. Small, Expansions and Asymptotics for Statistics (Chapman & Hall, 2010). doi: 10.1201/9781420011029.
- [13] T.L. Toulias and C.P. Kitsos, On the generalized Lognormal distribution, J. Prob. and Stat. (2013) 1-16. doi: 10.1155/2013/432642.
Typ dokumentu
Bibliografia
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DOI
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1154