Global approximations for the γ-order Lognormal distribution
Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) no. 1-2.

Voir la notice de l'article dans Library of Science

A generalized form of the usual Lognormal distribution, denoted with _γ, is introduced through the γ-order Normal distribution _γ, with its p.d.f. defined into (0,+∞). The study of the c.d.f. of _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.
Mots-clés : cumulative distribution function, γ-order Lognormal distribution, global Padé approximation
@article{DMPS_2013_33_1-2_a6,
     author = {Toulias, Thomas},
     title = {Global approximations for the \ensuremath{\gamma}-order {Lognormal} distribution},
     journal = {Discussiones Mathematicae Probability and Statistics},
     publisher = {mathdoc},
     volume = {33},
     number = {1-2},
     year = {2013},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a6/}
}
TY  - JOUR
AU  - Toulias, Thomas
TI  - Global approximations for the γ-order Lognormal distribution
JO  - Discussiones Mathematicae Probability and Statistics
PY  - 2013
VL  - 33
IS  - 1-2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a6/
LA  - en
ID  - DMPS_2013_33_1-2_a6
ER  - 
%0 Journal Article
%A Toulias, Thomas
%T Global approximations for the γ-order Lognormal distribution
%J Discussiones Mathematicae Probability and Statistics
%D 2013
%V 33
%N 1-2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a6/
%G en
%F DMPS_2013_33_1-2_a6
Toulias, Thomas. Global approximations for the γ-order Lognormal distribution. Discussiones Mathematicae Probability and Statistics, Tome 33 (2013) no. 1-2. https://geodesic-test.mathdoc.fr/item/DMPS_2013_33_1-2_a6/

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.

F. Bernardeau and L. Kofman, Properties of the cosmological density distribution function, Monthly Notices of the Royal Astrophys. J. 443 (1995) 479-498.

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.

E.L. Crow and K. Shimizu, Lognormal Distributions - Theory and Applications (M. Dekker, New York Basel, 1998).

J. Gathen and J. Gerhard, Modern Computer Algebra (Cambridge University Press, 1993).

I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Elsevier, 2007).

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.

C.P. Kitsos and T.L. Toulias, New information measures for the generalized normal distribution, Information 1 (2010) 13-27. doi: 10.3390/info1010013.

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.

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.

T.J. Kozubowski and K. Podgórski, Asymmetric Laplace distributions, Math. Sci. 25 (2000) 37-46.

C.G. Small, Expansions and Asymptotics for Statistics (Chapman Hall, 2010). doi: 10.1201/9781420011029.

T.L. Toulias and C.P. Kitsos, On the generalized Lognormal distribution, J. Prob. and Stat. (2013) 1-16. doi: 10.1155/2013/432642.