The three diagnostic diagrams

library(logcumulant)
data(reliability_datasets)
yarn <- reliability_datasets$Yarn

The package provides three complementary moment-ratio diagrams. Each overlays the theoretical loci of the six reference families with a bootstrap cloud of the sample estimate and a 95% concentration ellipse.

Log-cumulant diagram

Plots $\kappa_3$ (log-skewness) against $\kappa_2$ (log-variance). The vertical axis $\kappa_3 = 0$ is where the symmetric-on-the-log-scale families (Log-Normal, Log-Logistic) lie.

log_cumulant_diagram(yarn, "Yarn", B = 300)

Kurtosis-skewness diagram

On the original scale: skewness $\gamma_3$ versus excess kurtosis $\gamma_4$, with the feasible-region boundary $\gamma_4 = \gamma_3^2 - 2$.

kurtosis_diagram(yarn, "Yarn", B = 300)

Coefficient-of-variation diagram

Coefficient of variation $\gamma_2$ versus skewness $\gamma_3$, again on the original scale.

cv_diagram(yarn, "Yarn", B = 300)

All three at once

three_diagrams(yarn, "Yarn", B = 300)

Several datasets on one diagram

multi_lc_diagram() overlays bootstrap clouds for several datasets, distinguished by colour and plotting symbol.

multi_lc_diagram(
  reliability_datasets[c("Airplane", "BallBearing", "Yarn")],
  B = 300
)