Ultra-fine transformation of data for normality

Abstract

Normally distributed data is crucial for the application of large-scale statistical analysis. To statisticians, the most important assumptions of statistical users are the adequacy of the data and the normal distribution of the data. However, users are constantly forced to deal with unusual data. This includes changing the method used to be less sensitive to non-normal data or transforming that data to normal data. In addition, common mathematical transformation methods (for example, Box-Cox) do not work on complex distributions, and each method works on limited data shapes. In this paper, a novel approach is presented to transform any data into normally distributed data. We refer to our approach as the Ultra-fine transformation method. The article's novelty is that the proposed approach is powerful enough to accurately transform any data with any distribution to the standard normal distribution. Besides this approach's usefulness, it is simple in both theory and in application, and users can easily retrieve the original data from its transformed state. Therefore, we recommend using this method for the data used in the statistical method, even if the data are normal.

Keywords

• Normal distribution
• Data normalization
• Transform for normality
• Ultra-fine transformation