Local Influence Diagnostics for the Extreme-Value Birnbaum-Saunders Regression Model

Local influence diagnostics for the Extreme-Value Birnbaum-Saunders (EVBS) regression model of Ferreira, Gomes and Leiva (2012): joint maximum likelihood estimation, conformal normal curvature diagnostics under case-weight, response and explanatory-variable perturbation, randomized quantile residuals with simulation envelope, the density, distribution and quantile functions, the finite upper endpoint, return levels and expected shortfall, moving-block bootstrap standard errors, a prospective index of endpoint identifiability, the same diagnostics for generalized extreme-value regression, and a 'gamlss' family allowing the tail-shape parameter to depend on covariates. The methods are described in Lima, Ospina, Barros and Macedo (2025) and are applied to monthly maximum wind gusts from Itajai, Brazil.

evbsreg

Local influence diagnostics for the Extreme-Value Birnbaum–Saunders (EVBS) regression model.

It provides joint maximum likelihood estimation, conformal normal curvature (CNC) diagnostics under three perturbation schemes, randomized quantile residuals with simulation envelope, the EVBS distribution family (density, distribution, quantile), the finite upper endpoint, return levels and expected shortfall, moving-block bootstrap standard errors, and the same local influence diagnostics for the generalized extreme-value (GEV) regression model, used as a benchmark. evbs_monitor() combines the curvature diagnostic with the finite upper endpoint into a prospective index of endpoint identifiability with a natural control limit. See NEWS.md for the changelog and the vignette for a reproducible walk-through.

The methodology is described in

Ospina, R., Lima, J. I. C., Barros, M., and Macêdo, A. M. S. (2026). Local influence diagnostics for extreme-value Birnbaum–Saunders regression, with an application to wind-gust extremes. Submitted. Preliminary version: arXiv:2507.22967.

Installation

From CRAN:

install.packages("evbsreg")

Or the development version from GitHub:

# install.packages("remotes")
remotes::install_github("Raydonal/evbsreg")

Dependencies: ggplot2 (density plots) besides base R. gamlss is needed only to fit the optional logEVBS() family with the gamlss package itself.

Quick start

library(evbsreg)
data(itajai)

# 1. Fit the EVBS regression model
X   <- cbind(1, itajai$pressure)
fit <- evbsreg.fit(X, itajai$wind)
round(fit$coeff, 4)

# 2. Local influence diagnostics
diag <- cnc_diagnostics(fit)
plot_cnc(diag, q = 7)

# 3. Most influential observation
which(diag$Bj[7, ] > diag$bq[7])

# 4. Refit without it and measure the impact
fit82 <- evbsreg.fit(X[-82, ], itajai$wind[-82])
round(100 * (fit82$coeff - fit$coeff) / abs(fit$coeff), 2)

The tail-shape parameter changes by about −73.67% when the catastrophic event of 26 April 2017 (observation 82) is removed, while the regression structure remains stable.

Main functions

Function	Purpose
`evbsreg.fit()`	Joint maximum likelihood fit of the EVBS regression model
`cnc_diagnostics()`	Conformal normal curvature diagnostics
`plot_cnc()`	Two-panel diagnostic figure (eigenvalues + contributions)
`rqrandomized()`, `rcoxsnell()`	Quantile and Cox–Snell residuals
`envelope_qq()`	Normal probability plot with simulation envelope
`revbs()`, `devbs()`, `pevbs()`, `qevbs()`	EVBS density, distribution, quantile, and random generation
`evbs_endpoint()`	Finite upper endpoint of the fitted model (Weibull domain)
`evbs_return_level()`	Return levels and expected shortfall from the EVBS quantile function
`evbs_block_boot()`	Moving-block bootstrap standard errors for serially dependent series
`evbsreg.fit.mc()`	Monte Carlo simulation study
`plot_evbs_alpha()` …	Density plots (Figures 1–2 of the paper)
`gevreg.fit()`, `gev_scores()`, `cnc_diagnostics_gev()`	GEV regression fit and matching local influence diagnostics
`logEVBS()`, `dlogEVBS()`, `plogEVBS()`, `qlogEVBS()`	`gamlss.family` for a log-EVBS model with covariate-dependent shape
`evbs_monitor()`, `plot.evbs_monitor()`	Prospective endpoint-identifiability control chart

See vignette("evbsreg") for the full worked example.

Reproducing the paper

Five standalone scripts reproduce every figure, table, and simulation:

source(system.file("scripts/script_01_density_figures.R",    package = "evbsreg"))
source(system.file("scripts/script_02_itajai_application.R", package = "evbsreg"))
source(system.file("scripts/script_03_simulation_scenario1.R", package = "evbsreg"))
source(system.file("scripts/script_04_simulation_scenario2.R", package = "evbsreg"))
source(system.file("scripts/script_05_simulation_scenario3.R", package = "evbsreg"))

Each simulation script defaults to m = 5000 replicates (matching the paper). Set m <- 500 at the top of a script for a quick check.

Documentation

Full documentation, including the reference index and the "Get started" vignette, is available at the package website: https://raydonal.github.io/evbsreg/.