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Drought frequency analysis provides valuable information for drought risk assessment. Nonparametric kernel density estimation (KDE) is applied for agricultural drought frequency analysis at the global scale. Agricultural drought over 1950–2020 is described by the standardized soil moisture index (SSMI), and drought variables (i.e., duration, severity, and peak) are extracted using run theory. The univariate and multivariate joint distributions of drought variables are established by KDE. Given that the averages for drought duration, severity, and peak are 3.10 (months), 1.59, and 0.60, respectively, the spatial distributions of multivariate return periods are mapped to determine regions with higher drought risk. The results showed that: (1) The mean values of drought duration, severity, and peak over different regions were in the ranges of 1.94–5.18 (months), 0.92–2.81, and 0.49–0.72, respectively. (2) Drought severity had higher correlations with drought duration (0.83) and peak (0.91), while the correlation coefficient between drought duration and peak was lower (0.73). (3) KDE can establish reliable joint distributions of drought variables after passing Kolmogorov-Smirnov (K S) and Anderson-Darling (A-D) tests at the 5% significance level with an average root-mean-square error of 0.04. (4) When the univariate return period was equal to 100 years, the multivariate joint return period of the "or" case was generally less than 70 years but that of the "and" case was mainly greater than 200 years. (5) Compared with other regions, West North America, North-East Brazil, Southeastern South America, Central Asia, and the Tibetan Plateau experienced higher drought risks. Accordingly, countermeasures should be established in these regions to alleviate drought impacts. [Display omitted] • Multivariate drought frequency analysis was carried out by applying nonparametric kernel density estimation (KDE) approach. • Drought return period in the "or" case was always shorter than that in the "and" case. • Drought risk was high in West North America, North-East Brazil, Southeastern South America, Central Asia and Tibetan Plateau. [ABSTRACT FROM AUTHOR]