Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

References

• Ahrens , L.H. 1954 . The lognormal distribution of elements . Geochimica et Cosmochimica Acta , 5 : 49 – 73 .
   Web of Science ®Google Scholar
• Aitchison , J. and Brown , J.A.C. 1969 . The Loqnormal Distribution , London : Cambridge University Press .
   Google Scholar
• Box , G.E.P. and Cox , D.R. 1964 . An analysis of transformations . J. Roy. Statist. Soc , 26 : 211 – 251 .
   Google Scholar
• Calitz , F. 1973 . Maximum likelihood estimation of the parameters of the three-parameter loqnormal distribution - a reconsideration . Austral. J. Statist , 3 : 185 – 190 .
   Google Scholar
• Cochran , W.G. 1938 . Some difficulties in the statistical analysis of replicated experiments . Empire Journal of Experimental Agriculture , 6 : 157 – 163 .
   Google Scholar
• Cohen , A.C. 1951 . Estimating parameters of logarithmic-normal distributions by maximum likeliho . J. Amer. Statist. Assoc , 46 : 206 – 212 .
   Web of Science ®Google Scholar
• Cohen , A.C. and Whitten , B.J. 1980 . Estimation in the three parameter lognormal distribution . J. Amer. Statist. Assoc , 75 : 399 – 404 .
   Web of Science ®Google Scholar
• D'Agostino , R.B. 1971 . An omnibus test of normality for moderate and large size samples . Biometrika , 58 : 341 – 348 .
   Web of Science ®Google Scholar
• Easterling , R.B. 1976 . Goodness-of-fit and parameter estimation . Technometrics , 18 : 1 – 9 .
   Web of Science ®Google Scholar
• Filliben , J.J. 1975 . The probability plot correlation coefficient test for normality . Technometrics , 17 : 111 – 117 .
   Web of Science ®Google Scholar
• Gibrat , R. 1931 . Les Inegalites Economiques , Paris : Libraire du Recueil Sirey .
   Google Scholar
• Giesbrecht , F. and Kempthorne , O. 1976 . Maximum likelihood estimation in the three-parameter lognormal distributi . J, Roy, Statist, Soc., B , 38 : 257 – 264 .
   Google Scholar
• Harter , H.L. 1961 . Expected values of normal order statistics . Biometrika , 48 : 151 – 165 .
   Web of Science ®Google Scholar
• Harter , H.L. and Moore , A.H. 1966 . Local maximum likelihood estimation of the parameters of three-parameter lognormal populations from complete and censored samples . J. Amer. Statist. Assoc , 61 : 842 – 851 .
   Web of Science ®Google Scholar
• Hill , B.M. 1963 . The three-parameter lognormal distribution and Bayesian analysis of a point-source epidemic . J. Amer. Statist. Assoc , 58 : 72 – 84 .
   Web of Science ®Google Scholar
• Johnson , N.L. and Kotz , S. 1970 . Continuous Univariate Distributions-1 , New York : John Wiley & Sons .
   Google Scholar
• Kane , V.E. 1979 . Fitting a three-parameter lognormal distribution with applications to hydrogeochemical data from the National Uranium Resource Evaluation Program , Oak Ridge, Tennessee : Union Carbide Corporation, Nuclear Division, Oak Ridge Gaseous Diffusion Plant . Technical Report K/UR-27
   Google Scholar
• Kempthorne , O. The classical problem of inference-goodness of fit . Proceedings of the Fifth Berkeley Synposium . pp. 235 – 249 . 1
   Google Scholar
• Kinderman , A.J. and Ramage , J.G. 1976 . Computer generation of normal random variables . J. Amer. Statist. Assoc , 71 : 893 – 896 .
   Web of Science ®Google Scholar
• Kleczkowski , A. 1949 . The transformation of local lesion counts for statistical analysis . Annals of Applied Biology , 36 : 139 – 152 .
   PubMed Web of Science ®Google Scholar
• Lambert , J.A. 1964 . Estimation of parameters in the three-parameter lognormal distribution . Austral. J. Statist , 6 : 29 – 32 .
   Google Scholar
• Mann , N.R. , Schafer , R.E. and Singpurwalla , N.D. 1974 . Methods for Statistical Analysis of Reliability and kife Data , New York : John Wiley & Sons .
   Google Scholar
• Munro , A.H. and Wixley , R.A.J. 1970 . Estimators based on order statistics of small samples from a three-parameter lognormal distribution . J. Amer. Statist. Assoc , 65 : 212 – 225 .
   Web of Science ®Google Scholar
• Parr , W.C. and Schucany , W.R. 1980 . Minimum distance and robust estimation . J. Amer. Statist. Assoc , 75 : 616 – 624 .
   Web of Science ®Google Scholar
• Rao , P.V. , Schuster , E.F. and Littell , R.C. 1975 . Estimation of shift and center of symmetry based on Kolmogorov-Smirnov statistics . Ann. Statist , 2 : 862 – 873 .
   Google Scholar
• Sahler , S. 1970 . Estimation by minimum-discrepancy methods . Metrika , 15 : 85 – 106 .
   Web of Science ®Google Scholar
• Shapiro , S.S. and Francia , R.S. 1972 . An approximate analysis of variance test for normality . J. Amer. Statist. Assoc , 67 : 215 – 216 .
   Web of Science ®Google Scholar
• Shapiro , S.S. and Wilk , M.B. 1965 . An analysis of variance test for normality (complete samples) . Biometrika , 52 : 591 – 611 .
   Web of Science ®Google Scholar
• Stedinger , J.R. 1980 . Fitting lognormal distributions to hydrologic data . Water Resources Research , 16 : 481 – 490 .
   Web of Science ®Google Scholar
• Wilson , E.B. and Worcester , J. 1945 . The normal logarithmic transform . Review of Economic Statistics , 27 : 17 – 22 .
   Web of Science ®Google Scholar
• Wingo , D.R. 1975 . The use of interior penalty functions to overcome lognormal distribution parameter estimation anomalies . J. Statist. Comp. Simul , 4 : 49 – 61 .
   Google Scholar
• Wingo , D.R. 1976 . Moving truncations barrier-function methods for estimation in three-parameter lognormal models . Commun. Statist , B5 : 65 – 80 .
   Google Scholar