Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution

Mathematics and Computers in Simulation - Tập 54 - Trang 81-97 - 2000
Hideo Hirose1
1Department of Control Engineering and Science, Kyushu Institute of Technology, Iizuka, Fukuoka 820-8502, Japan

Tài liệu tham khảo

E.L. Allgower, K. Georg, Numerical Continuation Methods, Springer, Berlin, 1990. Bartlett, 1946, The statistical analysis of variance-heterogeneity and the logarithmic transformation, J. R. Stat. Soc., 8 (Suppl.), 128 Cheng, 1990, Embedded models in three-parameter distributions and their estimation, J. R. Stat. Soc., Ser. B, 52, 135 A.C. Cohen, B.J. Whitten, Parameter Estimation in Reliability and Life Span Models, Marcel Dekker, New York, 1988. Engelhardt, 1979, Prediction limits and two sample problems with complete or censored Weibull data, Technometrics, 21, 233, 10.2307/1268521 N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous Univariate Distributions, Vol. 1, Wiley, New York, 1994. Jones, 1978, Root isolation using function values, BIT, 18, 311, 10.1007/BF01930900 Hager, 1970, Inferential procedures for the generalized gamma distribution, J. Am. Stat. Soc., 65, 1601, 10.1080/01621459.1970.10481190 Harter, 1967, Maximum-likelihood estimation of the parameters of a four-parameter generalized gamma population from complete and censored samples, Technometrics, 9, 159, 10.2307/1266326 Harter, 1966, Local-maximum-likelihood estimation of the parameters of three-parameter lognormal populations from complete and censored samples, J. Am. Stat. Assoc., 61, 842, 10.2307/2282793 Hirose, 1994, Parameter estimation in the extreme-value distributions using the continuation method, Trans. Information Process. Soc. Jpn., 35, 1674 Hirose, 1997, Maximum likelihood estimation in the three-parameter log-normal distribution using the continuation method, Comput. Stat. Data Anal., 24, 139, 10.1016/S0167-9473(96)00063-1 Hirose, 1998, Parameter estimation for the 3-parameter gamma distribution using the continuation method, IEEE Transactions on Reliability, 47, 188, 10.1109/24.722287 Hirose, 1997, Inference from grouped data in three-parameter Weibull models with applications to breakdown-voltage experiments, Technometrics, 39, 199, 10.2307/1270908 Y. Kako, Estimation of Weibull parameters for BDV data of transformer oil by most likelihood methods, in: Conference Internationale des Grands Reseaux Electriques, Working Group 15-01, Task Force 02 (1986). Lambert, 1964, Estimation of parameters in the three-parameter lognormal distribution, Aust. J. Stat., 6, 29, 10.1111/j.1467-842X.1964.tb00248.x Lawless, 1980, Inference in the generalized gamma and log gamma distributions, Technometrics, 22, 409, 10.2307/1268326 J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 1982. Lieblein, 1956, Statistical investigation of the fatigue lift of deep-groove ball bearings, J. Res. Natl. Bureau Standards, 47, 273, 10.6028/jres.057.033 Lienhard, 1967, A physical basis for the generalized gamma distribution, Q. Math., 25, 330 Mees, 1984, La famille gamma generalisee: un modele de courbes de germination, Biometrie-Praximetrie, 24, 101 Parr, 1965, A method for discriminating between failure density functions used in reliability predictions, Technometrics, 7, 1, 10.2307/1266123 Pike, 1966, A suggested method of analysis of a certain class of experiments in carcinogenesis, Biometrics, 22, 142, 10.2307/2528221 Prentice, 1974, A log gamma model and its maximum likelihood estimation, Biometrika, 61, 539, 10.1093/biomet/61.3.539 Rockette, 1974, Maximum likelihood estimation with the Weibull model, J. Am. Stat. Soc., 69, 246, 10.1080/01621459.1974.10480164 Smith, 1985, Maximum likelihood estimation in a class of nonregular cases, Biometrika, 72, 67, 10.1093/biomet/72.1.67 Smith, 1987, A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution, Biometrika, 73, 67 Stacy, 1962, A generalization of the gamma distribution, Ann. Math. Stat., 33, 1187, 10.1214/aoms/1177704481 Stacy, 1965, Parameter estimation for a generalized gamma distribution, Technometrics, 7, 349, 10.2307/1266594 Stacy, 1973, Quasimaximum likelihood estimators for two-parameter gamma distributions, IBM J. Res. Dev., 17, 115, 10.1147/rd.172.0115 Wingo, 1987, Computing maximum-likelihood parameter estimates of the generalized gamma distribution by numerical root isolation, IEEE Trans. Reliability, R-36, 586, 10.1109/TR.1987.5222478