On the Construction of Multivariate Drought Indices: Theoretical Foundations and Practical Implications

Drought indices represent essential tools for monitoring and evaluating drought conditions and evolution. Univariate indices employ the Probability Integral Transform to map data onto the standard Gaussian domain. Extending such a Gaussian normalization procedure to multivariate settings requires the usage of the Kendall distribution function for preserving the Normality of the indices when aggregating the variables via their joint CDF. This work aims to clarify the issue and underscore the importance of applying proper standardization in multivariate frameworks. We show that neglecting this aspect can lead to biased estimation of drought occurrences, as illustrated through both theoretical and empirical analyses.