xnormalization

Xnormalization is a mathematical concept and statistical technique used to achieve a specific type of data standardization, where the zero point in a distribution is aligned to a standard threshold to facilitate comparisons and analysis. This method is particularly useful in multivariate analysis, where the distribution of multiple variables with varying scales can be difficult to comprehend.

In xnormalization, the distribution of each variable is adjusted so that its mean is zero and its standard deviation is a specified value, usually one. This process is often performed to scale variables to a common unit, enabling the comparison and combination of data across different variables.

The term "xnormalization" is an acronym for "eXtended normalization" which was introduced in 2010 as a complement to the usual standardization and normalization techniques that assume Gaussian or normal distributions. Xnormalization is an extension of these methods as it does not imply any distribution for the variable. It offers more flexibility in the analysis, especially when the assumption of normality is not met.

While xnormalization is used primarily for datasets with non-Gaussian distributions, and it can become tricky to interpret results from the transformed data. Nonetheless, xnormalization offers a method to analyze variables that would otherwise be difficult to compare or combine. Statistical techniques employing this concept often depend on implementing specialized algorithms which can normalize the variables to a standard scale before further analysis.