README

bgev

An R package for the bimodal GEV (Generalized Extreme Value) distribution: density, distribution, quantile, and random generation functions, plus maximum likelihood estimation. Useful for modeling heterogeneous bimodal data. The parametrization follows the revised BGEV with a location parameter of Otiniano, Lisboa & Ribeiro (2025) doi:10.3390/e27070749, which generalizes Otiniano et al. (2023) doi:10.1007/s10651-023-00566-7.

Installation

# install.packages("remotes")
remotes::install_github("thiagodoregosousa/bgev")

Usage

library(bgev)

set.seed(1)
x <- rbgev(n = 1000, mu = 0, sigma = 1, xi = 0.5, delta = 1)

hist(x, probability = TRUE, breaks = 30)
lines(sort(x), dbgev(sort(x), mu = 0, sigma = 1, xi = 0.5, delta = 1), col = "red")

fit <- bgev_mle(x)
fit$par          # estimated c(mu, sigma, xi, delta)
fit$admissible   # TRUE if the optimum is a regular (trustworthy) maximum

bgev_mle() returns the estimate together with diagnostics (convergence, agree, admissible, boundary, optimum). For discrete or rounded data use the grouped (interval) likelihood:

fit <- bgev_mle(round(x), likelihood = "grouped_likelihood", h = 1)

Estimation is restricted to delta > 0 (bimodality requires it, and delta < 0 makes the likelihood unbounded at x = mu); the distribution functions accept the full delta > -1. See the estimation vignette for the methodology and a Monte Carlo validation.

Functions

Function	Description
`dbgev()`	Density of the bimodal GEV distribution
`pbgev()`	Distribution function
`qbgev()`	Quantile function
`rbgev()`	Random generation
`bgev_mle()`	Maximum likelihood estimation with diagnostics
`bgev_log_likelihood()`	Log-likelihood used by `bgev_mle()`
`bgev_profile_likelihood()`	Profile log-likelihood for a parameter (diagnostic)
`bgev_valid_params()`	Check whether a set of parameters is valid
`bgev_support()`	Compute the support of the distribution for given parameters

Function

Description

dbgev()

Density of the bimodal GEV distribution

pbgev()

Distribution function

qbgev()

Quantile function

rbgev()

Random generation

bgev_mle()

Maximum likelihood estimation with diagnostics

bgev_log_likelihood()

Log-likelihood used by bgev_mle()

bgev_profile_likelihood()

Profile log-likelihood for a parameter (diagnostic)

bgev_valid_params()

Check whether a set of parameters is valid

bgev_support()

Compute the support of the distribution for given parameters

See the Reference page for full documentation.

Package layout

R/ — package source: distribution functions (bgev_distribution.R), support/validity (bgev_domain.R), estimation, starting values and diagnostics (bgev_estimation.R), and consistency checks (dist_check.R)

vignettes/ — estimation methodology write-up (bgev-estimation.Rmd)

man/, NAMESPACE — generated by devtools::document(); do not edit by hand

tests/testthat/ — unit tests, run via devtools::test()

benchmarks/ — Monte Carlo study (mc_study.R) and example datasets (data/), not part of the installed package

inst/shiny-app/ — interactive density explorer, run with shiny::runApp(system.file("shiny-app", package = "bgev"))

to_be_implemented/ — planned features not yet implemented

References

Otiniano, C. E. G., Lisboa, M. N. S., & Ribeiro, T. K. A. (2025). A Revised Bimodal Generalized Extreme Value Distribution: Theory and Climate Data Application. Entropy, 27(7), 749. doi:10.3390/e27070749

Otiniano, C. E. G., et al. (2023). A bimodal model for extremes data. Environmental and Ecological Statistics. doi:10.1007/s10651-023-00566-7