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2014 | 34 | 1-2 | 143-158
Tytuł artykułu

MLE for the γ-order Generalized Normal Distribution

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EN
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EN
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.
Twórcy
  • Technological Educational Institute of Athens, Greece
  • Democritus University of Thrace, Greece
  • Technological Educational Institute of Athens, Greece
Bibliografia
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  • [3] H. Alzer, On some inequalities for the incomplete gamma function, Mathematics of Computation 66 (228) (1997) 771-778. doi: 10.1090/S0025-5718-97-00814-4
  • [4] M. Chiodi, Sulle distribuzioni di campionamento delle stime di massima verosimiglianza dei parametri delle curve Normali di ordine p, Technical report, Istituto di Statistica, Facoltá di Economia e Commercio di Palermo 1988.
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  • [7] A.M. Mineo, Un nuovo metodo di stima di p per una corretta valutazione dei parametri di intensitá e di scala di una curva Normale di ordine p, in: Atti della XXXVII Riunione Scientifica della SIS, San Remo (Ed(s)), (1994, 147-154.
  • [8] A.M. Mineo and M. Ruggieri, A software tool for the exponential power distribution: The normalp package, J. Stat. Software (2005) 1-24.
  • [9] T.P. Minka, Old and new matrix algebra useful for statistics, Notes 2000.
  • [10] S.R. Searle, Matrix Algebra Useful for Statistics (New York, Wiley, 1982).
  • [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] 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.
  • [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] 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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1168
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