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2013 | 33 | 1-2 | 99-110
Tytuł artykułu

Global approximations for the γ-order Lognormal distribution

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EN
Abstrakty
EN
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.
Twórcy
  • 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.
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  • [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).
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  • [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.
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  • [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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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1154
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