Description

Extreme Value Modeling for r-Largest Order Statistics.

Description

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.

README.md

cran.r-project.org

evmr: Extreme Value Modeling for r-Largest Order Statistics

evmr

evmr is an R package for extreme value modeling using the r-largest order statistics framework.

The package provides tools for fitting, analyzing, and comparing extreme value models that use the largest r observations within each block.

The package is designed for applications in

hydrology
climatology
environmental science
extreme risk analysis

where multiple extreme events may occur within the same block.

Installation

# install.packages("remotes")
remotes::install_github("yire-shin/evmr")

Workflow

A typical workflow in evmr is

random generation → model fitting → return level estimation → profile likelihood → r selection

For each supported model, the package provides a consistent set of functions:

function	description
random generator	simulate r-largest order statistics
`.fit()`	fit the model by maximum likelihood
`.rl()`	estimate return levels
`.prof()`	obtain profile likelihood confidence intervals
`Edtest()`	perform entropy difference based sequential testing for selecting r

rK4D Model

The rK4D model is based on the four-parameter Kappa distribution.

Random generation

x <- rk4dr(
  n = 50, r = 3,
  loc = 10, scale = 2,
  shape1 = 0.1, shape2 = 0.1
)

head(x$rmat)

Model fitting

fit <- rk4d.fit(x$rmat, num_inits = 5)
fit$mle

Return levels

rk4d.rl(fit)

Profile likelihood confidence intervals

rk4d.prof(fit, m = 100, xlow = 12, xup = 25)

Entropy difference test for selecting r

rk4dEdtest(x$rmat)

Reference

Shin, Y., & Park, J.-S. (2023).
Modeling climate extremes using the four-parameter kappa distribution for r-largest order statistics.
Weather and Climate Extremes.
https://doi.org/10.1016/j.wace.2022.100533

Hosking, J. R. M. (1994).
The four-parameter Kappa distribution. Cambridge University Press.

Martins, E. S., & Stedinger, J. R. (2000).
Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data.
Water Resources Research.
https://doi.org/10.1029/1999WR900330

Coles, S., & Dixon, M. (1999).
Likelihood-based inference for extreme value models.
Extremes.
https://doi.org/10.1023/A:1009905222644

rGLO Model

The rGLO model is based on the generalized logistic distribution.

Random generation

x <- rglor(
  n = 50, r = 3,
  loc = 10, scale = 2,
  shape = 0.1
)

head(x$rmat)

Model fitting

fit <- rglo.fit(x$rmat, num_inits = 5)
fit$mle

Return levels

rglo.rl(fit)

Profile likelihood confidence intervals

rglo.prof(fit, m = 100, xlow = 12, xup = 25)

Entropy difference test for selecting r

rgloEdtest(x$rmat)

Reference

Ahmad et al. (1988).
Log-logistic flood frequency analysis.
Journal of Hydrology.
https://doi.org/10.1016/0022-1694(88)90015-7

Coles, S. (2001).
An Introduction to Statistical Modeling of Extreme Values.
Springer.
https://doi.org/10.1007/978-1-4471-3675-0

Shin, Y., & Park, J.-S. (2024).
Generalized logistic model for r-largest order statistics with hydrological application.
Stochastic Environmental Research and Risk Assessment.
https://doi.org/10.1007/s00477-023-02642-7

rGGD Model

The rGGD model is based on the generalized Gumbel distribution.

Random generation

x <- rggdr(
  n = 50, r = 3,
  loc = 10, scale = 2,
  shape = 0.1
)

head(x$rmat)

Model fitting

fit <- rggd.fit(x$rmat, num_inits = 5)
fit$mle

Return levels

rggd.rl(fit)

Profile likelihood confidence intervals

rggd.prof(fit, m = 100, xlow = 12, xup = 25)

Entropy difference test

rggdEdtest(x$rmat)

Reference

Coles, S. (2001).
An Introduction to Statistical Modeling of Extreme Values.
Springer.
https://doi.org/10.1007/978-1-4471-3675-0

Jeong et al. (2014).
A three-parameter kappa distribution with hydrologic application: A generalized Gumbel distribution.
https://doi.org/10.1007/s00477-014-0865-8

Shin, Y., & Park, J.-S. (2025).
Generalized Gumbel model for r-largest order statistics with application to peak streamflow.
Scientific Reports.
https://doi.org/10.1038/s41598-024-83273-y

rGD Model

The rGD model is based on the Gumbel distribution.

Random generation

x <- rgdr(
  n = 50, r = 3,
  loc = 10, scale = 2
)

head(x$rmat)

Model fitting

fit <- rgd.fit(x$rmat, num_inits = 5)
fit$mle

Return levels

rgd.rl(fit)

Profile likelihood confidence intervals

rgd.prof(fit, m = 100, xlow = 12, xup = 25)

Entropy difference test for selecting r

rgdEdtest(x$rmat)

Reference

Coles, S., & Dixon, M. (1999).
Likelihood-based inference for extreme value models.
Extremes.
https://doi.org/10.1023/A:1009905222644

Jeong et al. (2014).
A three-parameter kappa distribution with hydrologic application: A generalized Gumbel distribution.
https://doi.org/10.1007/s00477-014-0865-8

Shin, Y., & Park, J.-S. (2025).
Generalized Gumbel model for r-largest order statistics with application to peak streamflow.
Scientific Reports.
https://doi.org/10.1038/s41598-024-83273-y

rLD Model

The rLD model is based on the logistic distribution.

Random generation

x <- rldr(
  n = 50, r = 3,
  loc = 10, scale = 2
)

head(x$rmat)

Model fitting

fit <- rld.fit(x$rmat, num_inits = 5)
fit$mle

Return levels

rld.rl(fit)

Profile likelihood confidence intervals

rld.prof(fit, m = 100, xlow = 12, xup = 25)

Entropy difference test for selecting r

rldEdtest(x$rmat)

Reference

Ahmad et al. (1988).
Log-logistic flood frequency analysis.
Journal of Hydrology.
https://doi.org/10.1016/0022-1694(88)90015-7

Coles, S. (2001).
An Introduction to Statistical Modeling of Extreme Values.
Springer.
https://doi.org/10.1007/978-1-4471-3675-0

Unified Model Comparison Using Real Data

The package also provides a unified wrapper function, evmr(), for fitting multiple models simultaneously.

The following example uses the built-in bangkok dataset.

library(evmr)

data(bangkok)

evmr(
  bangkok,
  models = c("rk4d", "rglo", "rggd", "rgd", "rld"),
  num_inits = 5
)

This returns a combined summary table containing

model name
parameter estimates
likelihood values
standard errors
return level estimates

References

Ahmad et al. (1988).
Log-logistic flood frequency analysis.
Journal of Hydrology.
https://doi.org/10.1016/0022-1694(88)90015-7

Bader, B., Yan, J., & Zhang, X. (2017).
Automated selection of r for the r-largest order statistics approach.
Statistics and Computing.
https://doi.org/10.1007/s11222-016-9697-3

Coles, S. (2001).
An Introduction to Statistical Modeling of Extreme Values.
Springer.
https://doi.org/10.1007/978-1-4471-3675-0

Coles, S., & Dixon, M. (1999).
Likelihood-based inference for extreme value models.
Extremes.
https://doi.org/10.1023/A:1009905222644

Hosking, J. R. M. (1994).
The four-parameter Kappa distribution. Cambridge University Press.

Jeong et al. (2014).
A three-parameter kappa distribution with hydrologic application: A generalized Gumbel distribution.
https://doi.org/10.1007/s00477-014-0865-8

Shin, Y., & Park, J.-S. (2025).
Generalized Gumbel model for r-largest order statistics with application to peak streamflow.
Scientific Reports.
https://doi.org/10.1038/s41598-024-83273-y.

evmr: Extreme Value Modeling for r-Largest Order Statistics

evmr

Installation

Workflow

rK4D Model

Random generation

Model fitting

Return levels

Profile likelihood confidence intervals

Entropy difference test for selecting r

Reference

rGLO Model

Random generation

Model fitting

Return levels

Profile likelihood confidence intervals

Entropy difference test for selecting r

Reference

rGGD Model

Random generation

Model fitting

Return levels

Profile likelihood confidence intervals

Entropy difference test

Reference

rGD Model

Random generation

Model fitting

Return levels

Profile likelihood confidence intervals

Entropy difference test for selecting r

Reference

rLD Model

Random generation

Model fitting

Return levels

Profile likelihood confidence intervals

Entropy difference test for selecting r

Reference

Unified Model Comparison Using Real Data

References

Version

License

Status

Source

Homepage

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