Power Transformation and Its Modifications Toshimitsu HAMASAKI, Tatsuya ISOMURA, Megu OHTAKI and Masashi GOTO Key words : identity transformation, pow
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1 Power Transformation and Its Modifications Toshimitsu HAMASAKI, Tatsuya ISOMURA, Megu OHTAKI and Masashi GOTO Key words : identity transformation, power-normal distribution, structured data, unstructured data, regression analysis.179
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11 Atkinson, A.C., Pericchi, L.R. & Smith, R.L. (1991): Grouped likelihood for shifted power transformation. J. Roy. Statist. Soc. B53, Berry, D.A. (1987): Logarithmic transformation in ANOVA. Biometrics 43, Bickel, P.J. & Doksum, K.A. (1981): An analysis of transformations, revisited. J. Amer. Statist. Assoc. 76, Box, G.P.E & Cox, D.R. (1964): An analysis of transformations (with discussion). J. Roy. Statist. Soc. 189
12 B26, Box, G.P.E., Hunter, W.G. & Hunter, J.S. (1978) : Statistics for Experimenters. John Wiley & Sons. Carroll, R.J. (1980) : A robust method for testing transformations to achieve normality. J. Roy. Statist. Soc. B42, Chatterjee, S. & Price, B. (1991) : Regression Analysis by Example. 2nd edition, John Wiley & Sons. Cheng, R.C.H. & Traylor, L. (1995) : Non-regular maximum likelihood problems. J. Roy. Statist. Soc., B57, Cox, D.R. & Snell, E.J. (1981) : Applied Statistics : Principles and Examples. Chapman & Hall Cressie, N. (1978) : The exponential and power data transformation. The Statistician 27, Draper, D.R. & Hunter, W.G. (1969) : Transformations : Some examples revisited. Technometrics 11, Harris, E.K. & DeMets, D.L. (1972) : Estimation of normal ranges and cumulative proportion by trans forming observed distributions to Gaussian form. Clinical Chemistry 18, Hendl, J. (1987) : A note on exponential transformations. The Statistician 36, Hinkley D.V. & Runger, G. (1984) : The analysis of transformed data. J. Amer. Statist. Assoc. 79, Hoyle, M.H. (1973) : Transformations: An introduction and bibliography. Int. Stat. Rev. 41, Goto, M. (1992) : Extensive views of power transformation : Some recent developments. Invited paper of Honolulu Conference on Computational Statistics as Memorial of the Fifth Anniversary JSCS, JAMS, December, 1-5. Goto, M. (1995) : Double power transformations and their applications. Invited paper of International Conference on Statistical Computing for Quality and Productivity Improvement, Seoul, August, Goto, M., Matsubara, Y. & Tsuchiya, Y. (1983) : Power-normal distribution and its applications. Rep. Stat. Appl. Res., JUSE. 30(3), John, J.A. & Draper, N.R. (1980) : An alternative family of transformation. Appl. Statist. 29, Johnson, N.L., Kotz, S. & Balakrishnan, N. (1994) : Continuous Univariate Distributions. John Wiley & Sons. Kruskal, J.B. (1968) : Statistical analysis: Transformations of data. International Encyclopaedia of the Social. Science, The Macmillan Co. & the Free Press. Manly, B.F. (1976) : Exponential data transformation. The Statistician 25, Sakia, R.M. (1992) : The Box-Cox transformation technique: A review. The Statistician 41, Schlesselman, J. (1971) : Power families: Note on the Box and Cox transformation. J. Roy. Statist. Soc. B33, Snedecor, G.W. & Cochran, W. (1989) : Statistical Methods. 8th edition. Iowa State University Press. Snee, R.D. (1983) : Discussion on the paper by Professor Hocking. Technometrics 25,
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