A Quantile General Index Derived from the Maximum Entropy Principle

We propose a linear separation method of multivariate quantitative data in such a way that the average of each variable in the positive group is larger than that of the negative group. Here, the coefficients of the separating hyperplane are restricted to be positive. Our method is derived from the maximum entropy principle. The composite score obtained as a result is called the quantile general index. The method is applied to the problem of determining the top 10 countries in the world based on the 17 scores of the Sustainable Development Goals (SDGs).