A Comparison of Data Transformation Methods of Generalized Exponential Distribution and Estimation of Summer Rainfall in Chiang Dao, Chiang Mai
Abstract
This study aims to compare the efficiency of the data transformation methods of generalized exponential distribution simulated with different sample size and parameters. Transformation methods including Box-Cox power transformation, Cube-Root transformation ( ) and Fourth-Root transformation ( ) improve to investigate method of data transformation can transform data to normalizing data. By comparing a percentage of accept the null hypothesis (H0): the 10,000 repeated that data after transformation of the normal distribution are computed through the Monte Carlo technique. The simulation study’s results show that Fourth-Root transformation gives a highest percentage of accept the null hypothesis. These methods apply to determine the confidence interval of rain in summer season at gauging station, Chiang Dao district, Chiang Mai, Thailand. Annually, the mean values are between 254.0344 mm. and 340.1977 mm. at 95% confidence level. Keywords : generalized exponential distribution, Box-Cox transformation, Cube-Root transformation, Fourth-Root transformation, summer rainfallReferences
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Jirawan, P. (2011). Data The Efficiency Comparisons Among the Box-Cox Power Transformation Method and the New Power Transformation Method for Exponential Distribution. Faculty of Science. Chonburi: Burapha University. (in Thai)
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
Nopparat, K. (1999). Data Transformation to Normal Distribution. Faculty of Commerce and Accountancy. Bangkok: Chulalongkorn University. (in Thai)
Saithong, J. (2004). A Comparison of Efficiency of the Test Statistics for Goodness of Fit Test. Faculty of Science. Nakhonpathom: Silpakorn University. (in Thai)
Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association, 69, 730-737.
Box, G.E.P., Cox, D.R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society,
211-252.
Gupta, R. D., Kundu, D. (1999a). Generalized Exponential Distributions. Austral. N. Z. J. Statist, 41,173–188.
Jirawan, P. (2011). Data The Efficiency Comparisons Among the Box-Cox Power Transformation Method and the New Power Transformation Method for Exponential Distribution. Faculty of Science. Chonburi: Burapha University. (in Thai)
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
Nopparat, K. (1999). Data Transformation to Normal Distribution. Faculty of Commerce and Accountancy. Bangkok: Chulalongkorn University. (in Thai)
Saithong, J. (2004). A Comparison of Efficiency of the Test Statistics for Goodness of Fit Test. Faculty of Science. Nakhonpathom: Silpakorn University. (in Thai)
Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association, 69, 730-737.
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Published
2017-10-04
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Research Article
