Application of Transformation Techniques to Evaluate Drought
Abstract
The objective of this research was to compare data transformation methods, as well as to find the best data transformation technique for applying the standardized precipitation index to evaluate drought. Results of this study were as follows: part I was simulated data, Fourth-Root transformation was the best normal approximate transformation of gamma data. The Logarithm transformation was the best normal approximate transformation of lognormal data. The Haynes transformation was the best normal approximate transformation of Weibull data. Part II was real data, based on rain gauging stations of Ban Hong and Lee, Lamphun, Thailand to evaluate drought. Weibull distribution was found to be the most appropriate distribution to represent the Thai season rainfall amount in Ban Hong. Gamma distribution was found to be the most appropriate distribution to represent the Thai season rainfall amount in Lee. Ban Hong had extremely dry conditions in 2005 and 2014. Lee had extremely dry conditions in 1980, 2004, 2005 and 2014. Keywords Transformation, Standardized Precipitation IndexReferences
Agro - meteorological Academic Group Meteorological Development Bureau. (2011). Study on Drought Index in Thailand. Retrieved September 10, 2015, from http://tmd.go.th. (in Thai)
Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, 26(2), 211-252.
Bickel, P.J. and Doksum, K.A. (1981). An analysis of transformations revisited. Journal of the American Statistical Association. 76, 296- 311
Krishnamoorthy, K., Mathew, T. and Mukherjee, S. (2008). Normal-Based Methods for a Gamma Distribution: Prediction and Tolerance Intervals and Stress-Strength Reliability. American Statistical Association and the American Society for Quality, 50(1), 69-78.
Haynes, R. (2011). Transformation of Weibull Distribution Data A surprising result. Smarter Solutions, 1-10
Manly, B. F. J. (1976). Exponential Data Transformations. Statistician, 25(1), 37-42.
McKee, T.B., Doesken, N.J. and Kleist, J. 1993. The relationship of drought frequency and duration on time scale. Eighth Conf on Applied Climatology, 179–184.
Ngamjarus, C. (2001). The Comparison of Transformation Methods for Exponential Data to Normal Data. Bangkok : King Mongkut’s University of technology North Bangkok.(in Thai)
Thai Meteorological Department. (2015). Drought. Retrieved September 10, 2015, from http://www.tmd.go.th /info/ info.php?FileID=71 (in Thai)
Watthanacheewakul, L. (2014). A New Family of Transformations for Lifetime Data. In Proceedings of the World Congress on Engineering. United Kingdom: London.
Yeo, I. and Johnson, N. R. (2000). A new family of power transformations to improve normality or symmetry. Biometrika, 87(2), 954-959.
Yusof, F.and Hui-Mean, F. (2012). Use of statistical distribution for drought analysis. Applied Math Sci, 6(21), 1031–1051.
Zhang, Q., Xu, C.Y. and Zhang, Z. (2009). Observed changes of drought wetness episodes in the Pearl River Basin, China, using the standardized precipitation index and aridity index. Theor Appl Climatol, 98,89–99.
Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, 26(2), 211-252.
Bickel, P.J. and Doksum, K.A. (1981). An analysis of transformations revisited. Journal of the American Statistical Association. 76, 296- 311
Krishnamoorthy, K., Mathew, T. and Mukherjee, S. (2008). Normal-Based Methods for a Gamma Distribution: Prediction and Tolerance Intervals and Stress-Strength Reliability. American Statistical Association and the American Society for Quality, 50(1), 69-78.
Haynes, R. (2011). Transformation of Weibull Distribution Data A surprising result. Smarter Solutions, 1-10
Manly, B. F. J. (1976). Exponential Data Transformations. Statistician, 25(1), 37-42.
McKee, T.B., Doesken, N.J. and Kleist, J. 1993. The relationship of drought frequency and duration on time scale. Eighth Conf on Applied Climatology, 179–184.
Ngamjarus, C. (2001). The Comparison of Transformation Methods for Exponential Data to Normal Data. Bangkok : King Mongkut’s University of technology North Bangkok.(in Thai)
Thai Meteorological Department. (2015). Drought. Retrieved September 10, 2015, from http://www.tmd.go.th /info/ info.php?FileID=71 (in Thai)
Watthanacheewakul, L. (2014). A New Family of Transformations for Lifetime Data. In Proceedings of the World Congress on Engineering. United Kingdom: London.
Yeo, I. and Johnson, N. R. (2000). A new family of power transformations to improve normality or symmetry. Biometrika, 87(2), 954-959.
Yusof, F.and Hui-Mean, F. (2012). Use of statistical distribution for drought analysis. Applied Math Sci, 6(21), 1031–1051.
Zhang, Q., Xu, C.Y. and Zhang, Z. (2009). Observed changes of drought wetness episodes in the Pearl River Basin, China, using the standardized precipitation index and aridity index. Theor Appl Climatol, 98,89–99.
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Published
2016-06-21
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