evmr

Extreme Value Modeling for r-Largest Order Statistics

Tools for extreme value modeling based on the r-largest order statistics framework. The package provides functions for parameter estimation via maximum likelihood, return level estimation with standard errors, profile likelihood-based confidence intervals, random sample generation, and entropy difference tests for selecting the number of order statistics r. Several r-largest order statistics models are implemented, including the four-parameter kappa (rK4D), generalized logistic (rGLO), generalized Gumbel (rGGD), logistic (rLD), and Gumbel (rGD) distributions. The rK4D methodology is described in Shin et al. (2022) <doi:10.1016/j.wace.2022.100533>, the rGLO model in Shin and Park (2024) <doi:10.1007/s00477-023-02642-7>, and the rGGD model in Shin and Park (2025) <doi:10.1038/s41598-024-83273-y>. The underlying distributions are related to the kappa distribution of Hosking (1994) <doi:10.1017/CBO9780511529443>, the generalized logistic distribution discussed by Ahmad et al. (1988) <doi:10.1016/0022-1694(88)90015-7>, and the generalized Gumbel distribution of Jeong et al. (2014) <doi:10.1007/s00477-014-0865-8>. Penalized likelihood approaches for extreme value estimation follow Martins and Stedinger (2000) <doi:10.1029/1999WR900330> and Coles and Dixon (1999) <doi:10.1023/A:1009905222644>. Selection of r is supported using methods discussed in Bader et al. (2017) <doi:10.1007/s11222-016-9697-3>. The package is intended for hydrological, climatological, and environmental extreme value analysis.

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