Title
Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution
Authors
H. Hirose
Source
Mathematics and Computers in Simulation, Vol.54, No.3, pp.81-97 (2000.11)
Abstract
Maximum likelihood parameter estimation becomes easy by augmenting the parameter space of the probability distribution. A newly proposed extended model of the four-parameter generalized gamma distribution includes the three-parameter generalized extreme-value distribution which includes the two-parameter Gumbel distribution. These relationships allow us to construct the maximum likelihood parameter estimation procedure from simpler models to more complex models. This method works successfully when the solution is located in the interior of the parameter space. The continuation method is used for the model augmentation. The likelihood equations for the four-parameter generalized gamma distribution does not always have solutions in the interior of the parameter space; the continuation method, however, leads us to find solutions on the boundary or at the corner of the parameter space.
Key Words
maximum likelihood estimation, model augmentation, continuation method, generalized extreme-value distribution, extreme-value distribution, Weibull distribution, extended gamma distribution, CONTINUATION METHOD, 3-PARAMETER, INFERENCE
Citation

　

Times Cited in Web of Science: 11

Times Cited in Scopus: 2

Times Cited in Google Scholar: 22

Inspec: 1

Mathematical Review: 1

Cited in Books: D.N.P. Murthy, M. Xie, R. Jiang, Weibull Models, Wiley (2004)

WoS: MATHEMATICS AND COMPUTERS IN SIMULATION 巻: 98 ページ: 18-30 発行: APR 2014; IEEE TRANSACTIONS ON IMAGE PROCESSING 巻: 22 号: 10 ページ: 3791-3806 DOI: 10.1109/TIP.2013.2262285 発行: OCT 2013; STATISTICAL PAPERS 巻: 53 号: 4 ページ: 833-848 DOI: 10.1007/s00362-011-0386-1 発行: NOV 2012; MATHEMATICS AND COMPUTERS IN SIMULATION 巻: 82 号: 5 ページ: 777-789 DOI: 10.1016/j.matcom.2011.05.014 発行: JAN 2012; IEEE TRANSACTIONS ON IMAGE PROCESSING 巻: 22 号: 10 ページ: 3791-3806 DOI: 10.1109/TIP.2013.2262285 発行: OCT 2013; STATISTICAL PAPERS 巻: 53 号: 4 ページ: 833-848 DOI: 10.1007/s00362-011-0386-1 発行: NOV 2012; MATHEMATICS AND COMPUTERS IN SIMULATION 巻: 82 号: 5 ページ: 777-789 DOI: 10.1016/j.matcom.2011.05.014 発行: JAN 2012; EEE TRANSACTIONS ON IMAGE PROCESSING Volume: 19 Issue: 2 Pages: 281-289 Published: FEB 2010; IEEE TRANSACTIONS ON IMAGE PROCESSING Volume: 17 1233-1250 AUG 2008; STATISTICAL PAPERS Volume: 49 455-469 JUL 2008; MATHEMATICS AND COMPUTERS IN SIMULATION 74 (6): 443-453 APR 30 2007; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 14 (1): 257-260 FEB 2007; MATHEMATICS AND COMPUTERS IN SIMULATION 70 (4): 227-234 DEC 1 2005; IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E86A (5): 1256-1265 MAY 2003

Cited in other journals: Vladimir Vaclavik, Robust 2006, Simulation study robustness...; On estimation in conditional heteroskedastic time series models under non-normal distributions, Statistical Papers, Springer