---
title: "QQ-Plot"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{QQ-Plot}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 4.5,
  fig.align = "center"
)
options(tibble.print_min = 6, tibble.print_max = 6)

modern_r <- getRversion() >= "4.1.0"
```

# Quantile-Quantile Plot

The package `AcceptReject` provides the function `qqplot.accept_reject()` which allows us to construct quantile-quantile plots to assess the goodness of fit of a probability distribution to a data sample. Similar to the function `plot.accept_reject()`, the function `qqplot.accept_reject()` is a generic function that accepts an object of class accept_reject as an argument, easily constructing the plot of theoretical quantiles of f against the sample quantiles (observed quantiles).

This function works efficiently, so that in large samples, the points are optimized to generate a more efficient plot, utilizing the [`scattermore`](https://CRAN.R-project.org/package=scattermore) library in `R`.

## General usage format:

```{r, eval = FALSE}
## S3 method for class 'accept_reject'
qqplot(
  x,
  alpha = 0.5,
  color_points = "#F890C2",
  color_line = "#BB9FC9",
  size_points = 1,
  size_line = 1,
  ...
)
```

+ `x`:	Object of the class accept_reject returned by the function `accept_reject()`.
+ `alpha`: Transparency of the points and reference line representing where the quantiles should be (theoretical quantiles).
+ `color_points`:	Color of the points (default is `"#F890C2"`).
+ `color_line`:	Color of the reference line (detault is `"#BB9FC9"`).
+ `size_points`: Size of the points (default is `1`).
+ `size_line`:  Thickness of the reference line (default is `1`).
+ `...`:	Additional arguments for the `quantile()` function. For instance, it's possible to change the algorithm type for quantile calculation.

# Examples

## Discrete case

```{r}
library(AcceptReject)
library(cowplot)
x <- accept_reject(
  n = 2000L,
  f = dbinom,
  continuous = FALSE,
  args_f = list(size = 5, prob = 0.5),
  xlim = c(0, 5)
)
a <- plot(x)
b <- qqplot(x)
plot_grid(a, b, ncol = 2)
```

## Continuous case

```{r}
# For n = 1000
y <- accept_reject(
  n = 1000L,
  f = dbeta,
  continuous = TRUE,
  args_f = list(shape1 = 2, shape2 = 2),
  xlim = c(0, 1)
)

# For many points (scattermore is used):
z <- accept_reject(
  n = 11e3,
  f = dbeta,
  continuous = TRUE,
  args_f = list(shape1 = 2, shape2 = 2),
  xlim = c(0, 1)
)

# Gráficos
a <- plot(y)
b <- qqplot(y)
c <- plot(z)
d <- qqplot(z)
plot_grid(a, b, ncol = 2)
plot_grid(c, d, ncol = 2)
```