logcumulant

logcumulant provides goodness-of-fit tests and diagnostic diagrams for positive-support reliability data, built on Mellin log-cumulants. It implements a family of three complementary Hotelling-type \eqn{T^2} statistics together with three moment-ratio-style diagrams, all calibrated by a parametric bootstrap for reliable finite-sample inference.

The package is built around a few design choices:

• Three nested tests. T2_(2,3) targets log-scale shape (dispersion and skewness); T2_(1,2,3) adds the entropy-related first log-cumulant; and T2_(1,...,6) exploits higher-order log-cumulants for tail discrimination.
• Bootstrap-first inference. The discrepancy covariance is typically ill-conditioned, so the asymptotic chi-squared reference is unreliable in finite samples; the parametric bootstrap restores correct size.
• Diagnostic diagrams. Log-cumulant, kurtosis-skewness, and coefficient-of-variation diagrams, each overlaying the theoretical loci of six reliability families with a bootstrap cloud and a 95% concentration ellipse.
• Six reliability families. Weibull, Frechet, Gamma, Inverse-Gamma, Log-Normal, and Log-Logistic, all fitted by maximum likelihood with a fast C++ core.

Installation

The package depends on a small set of CRAN packages. Install them first if needed:

install.packages(c("Rcpp", "RcppArmadillo", "MASS", "VGAM", "actuar",
                   "numDeriv", "goftest", "ggplot2", "gridExtra"))

Then install the development version from GitHub:

# install.packages("remotes")
# remotes::install_github("raydonal/logcumulant")
install.packages("logcumulant", repos = c('https://raydonal.r-universe.dev', 'https://cloud.r-project.org'))

remotes (or devtools) installs the required dependencies automatically.

A 30-second tour

library(logcumulant)
data(reliability_datasets)

bb <- reliability_datasets$BallBearing

# Quick log-cumulant diagram with bootstrap cloud
plot_lc(bb, B = 100)

# The three diagnostic diagrams
three_diagrams(bb, "Ball Bearing")

# Compare all six families (T2, AD, CvM, AIC with bootstrap p-values)
gof_compare_all(bb, use_bootstrap = TRUE)

When to use which tool

Goal	Function
Quick log-cumulant diagram	plot_lc()
Log-cumulant diagram (full control)	log_cumulant_diagram()
Kurtosis-skewness diagram	kurtosis_diagram()
Coefficient-of-variation diagram	cv_diagram()
All three diagrams together	three_diagrams()
Several datasets on one diagram	multi_lc_diagram()
The three T-squared statistics	T2_all()
Bootstrap p-values	T2_bootstrap()
Full model comparison	gof_compare_all()
Size / power simulation	size_study(), power_study()

Citation

If you use logcumulant in academic work, please cite:

Santos, C. C. F., Ospina, R., Espinheira, P., & Oliveira, M. (2025). Goodness-of-Fit Tests Based on Mellin Statistics for Reliability Data.

License

GPL-3.