Goodness-of-Fit Tests and Diagrams Based on Mellin Log-Cumulants.
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; andT2_(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")
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.