On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution

Computational Statistics and Data Analysis

Volumn 52, Issue 9, 2008, Pages 4502-4511

  Jukić, Dragan ^a   Benšić, Mirta ^a   Scitovski, Rudolf ^a  

^a JOSIP JURAJ STROSSMAYER UNIVERSITY OF OSIJEK   (Croatia)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; WEIBULL DISTRIBUTION;

DATA WEIGHTS; NONLINEAR WEIGHTED LEAST SQUARES ESTIMATE; THREE-PARAMETER WEIBULL DISTRIBUTION;

LEAST SQUARES APPROXIMATIONS;

EID: 42749087388     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2008.03.001     Document Type: Article

References (21)

1. Banks R.B. Growth and Diffusion Phenomena: Mathematical Frameworks and Applications (1994), Springer-Verlag, Berlin
2. Bates D.M., and Watts D.G. Nonlinear Regression Analysis and its Applications (1988), Wiley, New York
3. Björck Å. Numerical Methods for Least Squares Problems (1996), SIAM, Philadelphia
4. Burridge J. A note on maximum likelihood estimation for regression models using grouped data. J. R. Stat. Soc. Ser. B 43 (1981) 41-45
5. Cheng R.C.H., and Iles T.C. Embedded models in three-parameter distributions and their estimation. J. R. Stat. Soc. Ser. B 52 (1990) 135-149
6. Demidenko E.Z. Criteria for global minimum of sum of squares in nonlinear regression. Comput. Statis. Data Anal. 51 (2006) 1739-1753
7. Demidenko E.Z. Is this the least squares estimate?. Biometrika 87 (2000) 437-452
8. Dennis J.E., and Schnabel R.B. Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1996), SIAM, Philadelphia
9. Gill P.E., Murray W., and Wright M.H. Practical Optimization (1981), Academic Press, London
10. Hadeler K.P., Jukić D., and Sabo K. Least squares problems for Michaelis Menten kinetics. Math. Meth. Appl. Sci. 30 (2007) 1231-1241
11. Jukić D., Kralik G., and Scitovski R. Least squares fitting Gompertz curve. J. Comput. Appl. Math. 169 (2004) 359-375
12. Jukić D., Scitovski R., and Späth H. Partial linearization of one class of the nonlinear total least squares problem by using the inverse model function. Computing 62 (1999) 163-178
13. Lawless J.F. Statistical Models and Methods for Lifetime Data (1982), Wiley, New York
14. Murthy D.N.P., Xie M., and Jiang R. Weibull Models (2004), Wiley, New York
15. Nelson W. Applied Life Data Analysis (1982), Wiley, New York
16. Pratt J.W. Concavity of the log likelihood. J. Amer. Statist. Assoc. 76 (1981) 103-106
17. Ross G.J.S. Nonlinear Estimation (1990), Springer, New York
18. Seber G.A.F., and Wild C.J. Nonlinear Regression (1989), Wiley, New York
19. Smith R.L., and Naylor J.C. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Biometrika 73 (1987) 67-90
20. Weibull W. A statistical theory of the strength of material. Ingen. Vetensk. Acad. Handl. 151 (1939) 1-45
21. Weibull W. A statistical distribution function of wide applicability. J. Appl. Mech. 18 (1951) 293-296