MLE for the γ-order Generalized Normal Distribution

Christos P. Kitsos; Vassilios G. Vassiliadis; Thomas L. Toulias

Discussiones Mathematicae Probability and Statistics (2014)

  • Volume: 34, Issue: 1-2, page 143-158
  • ISSN: 1509-9423

Abstract

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The introduced three parameter (position μ, scale ∑ and shape γ) multivariate generalized Normal distribution (γ-GND) is based on a strong theoretical background and emerged from Logarithmic Sobolev Inequalities. It includes a number of well known distributions such as the multivariate Uniform, Normal, Laplace and the degenerated Dirac distributions. In this paper, the cumulative distribution, the truncated distribution and the hazard rate of the γ-GND are presented. In addition, the Maximum Likelihood Estimation (MLE) method is discussed in both the univariate and multivariate cases and asymptotic results are presented.

How to cite

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Christos P. Kitsos, Vassilios G. Vassiliadis, and Thomas L. Toulias. "MLE for the γ-order Generalized Normal Distribution." Discussiones Mathematicae Probability and Statistics 34.1-2 (2014): 143-158. <http://eudml.org/doc/270919>.

@article{ChristosP2014,
abstract = {The introduced three parameter (position μ, scale ∑ and shape γ) multivariate generalized Normal distribution (γ-GND) is based on a strong theoretical background and emerged from Logarithmic Sobolev Inequalities. It includes a number of well known distributions such as the multivariate Uniform, Normal, Laplace and the degenerated Dirac distributions. In this paper, the cumulative distribution, the truncated distribution and the hazard rate of the γ-GND are presented. In addition, the Maximum Likelihood Estimation (MLE) method is discussed in both the univariate and multivariate cases and asymptotic results are presented.},
author = {Christos P. Kitsos, Vassilios G. Vassiliadis, Thomas L. Toulias},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {γ-order Normal distribution; cumulative distribution; truncated distribution; hazard rate; Maximum likelihood estimation; -order normal distribution; maximum likelihood estimation},
language = {eng},
number = {1-2},
pages = {143-158},
title = {MLE for the γ-order Generalized Normal Distribution},
url = {http://eudml.org/doc/270919},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Christos P. Kitsos
AU - Vassilios G. Vassiliadis
AU - Thomas L. Toulias
TI - MLE for the γ-order Generalized Normal Distribution
JO - Discussiones Mathematicae Probability and Statistics
PY - 2014
VL - 34
IS - 1-2
SP - 143
EP - 158
AB - The introduced three parameter (position μ, scale ∑ and shape γ) multivariate generalized Normal distribution (γ-GND) is based on a strong theoretical background and emerged from Logarithmic Sobolev Inequalities. It includes a number of well known distributions such as the multivariate Uniform, Normal, Laplace and the degenerated Dirac distributions. In this paper, the cumulative distribution, the truncated distribution and the hazard rate of the γ-GND are presented. In addition, the Maximum Likelihood Estimation (MLE) method is discussed in both the univariate and multivariate cases and asymptotic results are presented.
LA - eng
KW - γ-order Normal distribution; cumulative distribution; truncated distribution; hazard rate; Maximum likelihood estimation; -order normal distribution; maximum likelihood estimation
UR - http://eudml.org/doc/270919
ER -

References

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  11. [11] C.P. Kitsos and N.K. Tavoularis, Logarithmic Sobolev inequalities for information measures, IEEE Trans. Inform. Theory 55 (6) (2009) 2554-2561. doi: 10.1109/TIT.2009.2018179 
  12. [12] C.P. Kitsos, T.L. Toulias and C.P. Trandafir, On the multivariate γ-ordered normal distribution, Far East J. of Theoretical Statistics 38 (1) (2012) 49-73. Zbl1252.60020
  13. [13] G. Lunetta, Di alcune distribuzioni deducibili da una generalizzazione dello schema della curva Normale, Annali della Facoltá di Economia e Commercio di Palermo 20 (1966) 119-143. 
  14. [14] D.N. Naik and K. Plungpongpun, A Kotz-Type distribution for multivariate statistical inference, Statistics for Industry and Technology (2006) 111-124. doi: 10.1007/0-8176-4487-3_7. Zbl05196666

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