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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cre],
Jeong-Soo Park