Comparison of Four Data Transformation Methods for Weibull Distributed Data

Abstract

               The objective of this research was to compare four data transformation methods: the error function transformation, the dual power transformation, the exponential transformation of Manly, and the Box-Cox transformation. The criterion used for the study was the ratio of the percentage of acceptances of the null hypothesis H₀ to the data having a normal distribution, after the four data transformation methods were applied to Weibull distributed data. The approaches were evaluated using both real and simulated data. For the simulated data, Weibull distributed datasets were generated for skewness and kurtosis levels using MATLAB version 7.0 with three levels of sample size (n): small (10, 30), medium
(50, 70) and large (100, 120). Each situation was repeated 500 times and the significance level was set at 0.05.

                The results consisted of two parts: part I presented the simulated data and part II the real data. With the simulated data with right-skew distribution, and n=10, for skewness (0.3, 0.6], the Box-Cox and exponential transformation methods were the best methods, for skewness (0.6, 1.2], the Box-Cox method was the best and for skewness (1.2, 2.1], the Box-Cox and exponential transformation methods were the best methods. When n=30, 50, 70, 100 and 120, the Box-Cox method was the best. When the data had left-skew distribution, for small and medium sample sizes, the exponential transformation method was the best method for almost all situations. However, for a large sample size, the Box-Cox method was generally the best method. 

                 For the real data, the P-values and the histogram of the empirical data were presented. It was also found that the best transformation method was the Box-Cox method.