GLBFP
General Linear Blend Frequency Polygon Density Estimation
Implements nonparametric density estimation with Averaged Shifted
Histogram (ASH), Linear Blend Frequency Polygon (LBFP), and General Linear
Blend Frequency Polygon (GLBFP) estimators. The package provides pointwise
and grid-based estimation workflows, sparse-prefix grid-count computation,
plotting helpers, and plug-in bandwidth selection. Methodological
background follows Scott (1992)
GLBFP
GLBFP is an R package for histogram-based nonparametric density
estimation. It implements:
- Averaged Shifted Histogram estimators:
ASH(),ASH_estimate() - Linear Blend Frequency Polygon estimators:
LBFP(),LBFP_estimate() - General Linear Blend Frequency Polygon estimators:
GLBFP(),GLBFP_estimate()
The package supports pointwise density estimation, regular-grid estimation, 1D and 2D plotting, sparse-prefix grid-count computation, S3 summaries and predictions, and plug-in bandwidth selection.
Status
The package is prepared for CRAN submission. Development-only features remain on GitHub until their methodology and documentation are ready for release.
Installation
Install the development version from GitHub:
install.packages("remotes")
remotes::install_github("AurelienNicosiaULaval/GLBFP")
If the package is accepted on CRAN, installation will use:
install.packages("GLBFP")
Quick start
library(GLBFP)
set.seed(2026)
x <- matrix(rnorm(300), ncol = 1)
b <- compute_bi_optim(x, m = 1)
fit <- glbfp(x = 0, data = x, b = b, m = 1)
fit
summary(fit)
predict(fit)
Uppercase function names remain available and are the historical API:
fit_upper <- GLBFP(x = 0, data = x, b = b, m = 1)
identical(fit$estimation, fit_upper$estimation)
Two-dimensional workflow
library(GLBFP)
data("ashua")
river_data <- ashua[, c("flow", "level")]
b <- c(8, 0.4)
x0 <- c(mean(river_data$flow), mean(river_data$level))
point_fit <- glbfp(x = x0, data = river_data, b = b, m = c(1, 1))
point_fit
grid_fit <- glbfp_estimate(
data = river_data,
b = b,
m = c(1, 1),
grid_size = 20
)
summary(grid_fit)
head(as.data.frame(grid_fit))
plot(grid_fit, contour = TRUE)
Main functions
| Task | Functions |
|---|---|
| Pointwise density estimation | ASH(), LBFP(), GLBFP() |
| Grid-based density estimation | ASH_estimate(), LBFP_estimate(), GLBFP_estimate() |
| Lowercase aliases | ash(), lbfp(), glbfp(), ash_estimate(), lbfp_estimate(), glbfp_estimate() |
| Bandwidth helper | compute_bi_optim() |
| Bandwidth constants | K_mi(), G_i(), compute_G_star() |
| S3 helpers | print(), summary(), predict(), plot(), as.data.frame() |
Documentation
The pkgdown site is organized as a reading path:
- Getting started with GLBFP
- Package overview and workflow map
- Brief methodological background
- Choosing between ASH, LBFP and GLBFP
- Two-dimensional density estimation
- Sparse-prefix computation
- Objects, summaries and plotting
- Validation and comparison
- Legacy estimation example
The first five articles introduce the package and the estimators. The next two articles document implementation diagnostics and S3 behavior. The validation article gives a lightweight reproducible benchmark, while the legacy vignette is kept for backward compatibility.
References
General background on frequency polygons, averaged shifted histograms, and multivariate density estimation is available in:
- Carbon, M., and Duchesne, T. (2024). Multivariate frequency polygon for stationary random fields. Annals of the Institute of Statistical Mathematics, 76(2), 263-287. doi:10.1007/s10463-023-00883-5.
- Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley. doi:10.1002/9780470316849.
- Terrell, G. R., and Scott, D. W. (1985). Oversmoothed Nonparametric Density Estimates. Journal of the American Statistical Association, 80(389), 209-214. doi:10.1080/01621459.1985.10477163.
The complete bibliographic record for the original GLBFP methodological article
has not yet been verified in this repository. It is tracked in
dev/references_to_verify.md and should be added before journal submission.
Citation
To cite the package from R:
citation("GLBFP")
The repository also includes CITATION.cff for software citation metadata.
Development checks
devtools::document()
devtools::test()
devtools::check()
rcmdcheck::rcmdcheck(args = c("--as-cran"))
Benchmarks are stored in benchmarks/ and are not run automatically during
R CMD check.
Contributing
Please use GitHub issues and pull requests: https://github.com/AurelienNicosiaULaval/GLBFP/issues
License
GPL (>= 3).