---
title: "The three diagnostic diagrams"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{The three diagnostic diagrams}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>",
                      fig.width = 7, fig.height = 5.2, dpi = 96)
```

```{r setup}
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.

```{r}
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 \(\gamma_4 = \gamma_3^2 - 2\).

```{r}
kurtosis_diagram(yarn, "Yarn", B = 300)
```

## Coefficient-of-variation diagram

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

```{r}
cv_diagram(yarn, "Yarn", B = 300)
```

## All three at once

```{r, fig.width = 12, fig.height = 4.2}
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.

```{r}
multi_lc_diagram(
  reliability_datasets[c("Airplane", "BallBearing", "Yarn")],
  B = 300
)
```