The Generalized Extreme Value Distribution with a Refined Parameter Identification Method Applied to Dry Spell Lengths in Northern Iraq

Abstract Extreme dry spells, though acknowledged in hydrology, remain poorly understood despite their socio-economic impacts, especially via drought. The generalized extreme value (GEV) distribution with three parameters is a versatile continuous probability distribution, yet conventional parameter estimation often fails to capture the true distribution of dry spell lengths (DSLs). This study introduces a refined method to improve GEV parameter identification by accounting for instability associated with statistical quantities derived from sample data. The novel parameter identification method includes parametric estimations using the mean, the mode, the median, the variance, the skewness, and the entropy, possibly refined by the generalized Tikhonov regularization technique with iterations. The notion of outliers is also redefined via a bounded support framework. This study evaluates seasonal variations in DSLs using 44 years (1975–2018) of daily precipitation data from a meteorological station in Northern Iraq’s steppe climate. Final parameter sets are selected based on Kolmogorov–Smirnov goodness-of-fit tests, revealing strong seasonal distinctions. The extreme DSL value of 59 days observed during the autumnal season of 2010 exceeds the end of the right tail to be classified as an outlier. For practical drought risk assessment, analysis is provided to integrate the specific impacts of extreme DSL anomalies on crop production in conjunction with conventional agricultural calendars, while also considering associated socio-economic consequences.