A Skewness–Kurtosis Adjusted Expansion of the Standardised Precipitation Index for Drought Analysis

ABSTRACT This study outlines the methodological basis of a skewness–kurtosis adjusted expansion of the classical SPI for characterising drought as a natural hazard. The proposed eXpanded SPI (X‐SPI) jointly considers skewness and kurtosis‐related behaviour within a probabilistic standardisation framework. In X‐SPI, skewness is represented by a median‐based shift term. Kurtosis‐related effects are represented by a variability‐driven re‐scaling term. This re‐scaling term is derived from the coefficient of variation ( C v ) and its generalised form. It also reflects the mean–standard deviation relationship of the observed series. The proposed X‐SPI was evaluated against both the classical SPI and the median‐adjusted M‐SPI using CDF behaviour, class‐threshold probabilities, relative deviations, class‐transition matrices, and year‐by‐year time‐series comparisons. The analysis used precipitation records from 148 meteorological stations across Türkiye for 1966–2020, with variability metrics computed from annual and multi‐scale accumulated precipitation totals. These metrics were used to integrate the shift and rescaling components into the standardisation step. Results from representative stations indicate that the proposed re‐scaling component can adjust the position of standardised values relative to conventional classification thresholds in response to station‐specific precipitation variability. The re‐scaling component can also modulate the net magnitude of the shift component. Consequently, drought/wetness class assignments may change in either direction depending on the local variability regime. Overall, the findings suggest that variability magnitude can be informative for interpreting classification sensitivity in SPI‐type indices, thereby supporting a more distribution‐sensitive monitoring framework for drought while preserving the operational structure of probabilistic standardisation.