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http://dx.doi.org/10.5351/KJAS.2006.19.2.283

Shift-Power Transformation  

Cho Ki-Jong (Division of Environmental Science and Ecological Engineering, Korea University)
Jeong Seok-Oh (Department of Statistics, Hankuk University of Foreign Studies)
Shin Key-Il (Department of Statistics, Hankuk University of Foreign Studies)
Publication Information
The Korean Journal of Applied Statistics / v.19, no.2, 2006 , pp. 283-290 More about this Journal
Abstract
Generally speaking, power transformations such as Box-Cox transformation(1964) is applied for variance stabilization and symmetry. But, when the distribution of the original data has a large mean with a small variance or the coefficient of variation is very small, they don't work at all. This paper propose a simple method to introduce a shift parameter before applying power transformations and showed the numerical evidence by Monte Carlo simulation and a real data analysis.
Keywords
Power transformation; shifted power transformation; Box-Cox transformation; shift parameter;
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1 Atkinson, A. C., Pericchi, L. R. and Smith, R. L. (1991). Grouped likelihood for the shifted power transformation, Journal of the Royal Statistical Society B 53, 473-482
2 Park, H. and Shin, K.-I. (2006). A shrinked forecast in stationary processes favouring percentage error, Journal of Time Series Analysis 27, 129-139   DOI   ScienceOn
3 Shin, K.-I. and Kang, H. (2001). A study of the effect of power transformation in the ARMA(p,q) model, Journal of Applied Statistics 28, 1019-1028   DOI
4 Yeo, I.-K. and Johnson, R. A. (2000). A new family of power transformations to improve normality or symmetry, Biometrika 87, 954-959   DOI   ScienceOn
5 Bickel, P. J. and Doksum, K. A. (1981). An analysis of transformations revisited, Journal of the American Statistical Association 76, 296-311   DOI
6 Hernandez, F. and Johnson, R. A. (1980). The large-sample behavior of transformations to normality, Journal of the American Statistical Association 75, 855-861   DOI
7 Bloch, D. A. and Gastwirth, J. L. (1968). On a simple estimate of the reciprocal of the density function, Annals of Mathematical Statistics 39, 1083-1085   DOI
8 Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations (with Discussion), Journal of the Royal Statistical Society B 26, 211-252
9 Cochran, W. G. (1977), Sampling Techniques. 3rd edition, Wiley