Tail weighted multi criteria probability distribution selection for drought frequency analysis

Drought is a complex hydroclimatic hazard whose probabilistic characterization is strongly influenced by the drought index and probability distribution adopted. This study develops a distribution-sensitive framework for assessing drought frequency and long-term trends in the Zayandehrud Basin, Iran. Five 12-month drought indices, including SPI, SPEI, EDDI, RDI, and PDSI, were evaluated at seven meteorological stations during 1993–2024. Eighteen candidate probability distributions representing classical, generalized, heavy-tailed, extreme-value, and bounded-support families were fitted independently to each station–index series. Distribution selection was performed using a tail-weighted composite goodness-of-fit criterion integrating AIC, BIC, KS, standard Anderson–Darling, lower- and upper-tail Anderson–Darling statistics, and cross-validated log-likelihood. Bootstrap resampling and Q–Q plots were additionally used to assess fitting stability and graphical adequacy. The results revealed substantial spatial and inter-index distributional variability, with Cauchy frequently selected for EDDI and Beta commonly identified for PDSI, while RDI, SPEI, and SPI exhibited greater distributional diversity. Return-period analysis demonstrated increasing spatial divergence toward rarer drought events, emphasizing the importance of distributional uncertainty in extreme drought estimation. Trend analysis further revealed localized and index-dependent changes rather than a uniform basin-wide trend. The proposed framework provides a robust basis for drought-frequency assessment and supports location-specific drought-risk management and water-resources planning.