# 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

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topChristos 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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