Fitting Distribution to Data by a Generalized Nonlinear Least Squares Method

References

• Abbasi , B. , Jahromi , A. D. H. E. , Arkat , J. and Hosseinkouchack , M. 2006 . Estimating the parameters of Weibull distribution using simulated annealing algorithm . Applied Mathematics and Computation , 183 : 85 – 93 .
   Web of Science ®Google Scholar
• Ahmad , K. E. 1994 . Modified weighted least-squares estimators for the three-parameter Weibull distribution . Applied Mathematics Letters , 7 : 53 – 56 .
   Web of Science ®Google Scholar
• Al-Baidhani , P. A. and Sinclair , C. D. 1987 . Comparison of methods of estimation of parameters of the Weibull distribution . Communications in Statistics - Simulation and Computation , 16 : 373 – 384 .
   Web of Science ®Google Scholar
• Anderson , T. W. and Darling , D. A. 1952 . Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes . The Annals of Mathematical Statistics , 23 : 193 – 212 .
   Google Scholar
• Burridge , J. 1981 . A note on maximum likelihood estimation for regression models using grouped data . Journal of the Royal Statistical Society Series B , 43 : 41 – 45 .
   Google Scholar
• Castillo , J. and Daoudi , J. 2009 . Estimation of the generalized Pareto distribution . Statistics and Probability Letters , 79 : 684 – 688 .
   Web of Science ®Google Scholar
• Ivanov , A. V. 1976 . An asymptotic expansion for the distribution of the least squares estimator of the nonlinear regression parameter . Theory of Probability and its Applications , 21 : 557 – 570 .
   Web of Science ®Google Scholar
• Jukić , D. , Benšić , M. and Scitovski , R. 2008 . On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution . Computational Statistics & Data Analysis , 52 : 4502 – 4511 .
   Web of Science ®Google Scholar
• Littell , R. C. , Mc Clave , J. T. and Offen , W. W. 1979 . Goodness-of-fit tests for the two parameter Weibull distribution . Communications in Statistics - Simulation and Computation , 8 : 257 – 269 .
   Web of Science ®Google Scholar
• Luceño , A. 2006 . Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimator . Computational Statistics & Data Analysis , 51 : 904 – 917 .
   Web of Science ®Google Scholar
• Murthy , D. N. P. , Bulmerc , M. and Ecclestonc , J. A. 2004a . Weibull model selection for reliability modelling . Reliability Engineering and System Safety , 86 : 257 – 267 .
   Web of Science ®Google Scholar
• Murthy , D. N. P. , Xie , M. and Jiang , R. 2004b . Weibull Models , New York : John Wiley & Sons .
   Google Scholar
• Pollard , D. 1980 . The minimum distance method of testing . Metrika , 27 : 43 – 70 .
   Google Scholar
• Pratt , J. W. 1981 . Concavity of the log likelihood . Journal of the American Statistical Association , 76 : 103 – 106 .
   Web of Science ®Google Scholar
• Rinne , H. 2009 . The Weibull Distribution. A Handbook , Boca Raton : Chapman & Hall/CRC .
   Google Scholar
• Seber , G. A. F. and Wild , C. J. 1989 . Nonlinear Regression , New York : John Wiley & Sons .
   Google Scholar
• Shao , J. 1999 . Mathematical Statistics , New York : Springer-Verlag .
   Google Scholar
• Shier , D. R. and Lawrence , K. D. 1984 . A comparison of robust regression techniques for the estimation of Weibull parameters . Communications in Statistics - Simulation and Computation , 13 : 743 – 750 .
   Web of Science ®Google Scholar
• Shuhe , H. 2004 . Consistency for the least squares estimator in nonlinear regression model . Statistics & Probability Letters , 67 : 183 – 192 .
   Web of Science ®Google Scholar
• Smith , R. L. and Naylor , J. C. 1987 . A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution . Biometrika , 73 : 67 – 90 .
   Google Scholar
• Soman , K. P. and Misra , K. B. 1992 . A least square estimator of three parameters of a Weibull distribution . Microelectronics Reliability , 32 : 303 – 305 .
   Web of Science ®Google Scholar
• Weibull , W. 1939 . A statistical theory of the strength of material . Ingeniors Vetenskapa Acadamiens Handligar , 151 : 1 – 45 .
   Google Scholar
• Wolfowitz , J. 1953 . Estimation by minimum distance method . Annals of the Institute of Statistical Mathematics , 5 : 9 – 23 .
   Google Scholar
• Wolfowitz , J. 1957 . The minimum distance method . The Annals of Mathematical Statistics , 28 : 75 – 88 .
   Google Scholar