index.Rmd

--- 
title: "R Lab for Statistical Computing"
author: |
  | [Young-geun Kim](https://github.com/ygeunkim)
  | [Department of Statistics](https://stat.skku.edu/stat/index.jsp), [SKKU](https://www.skku.edu/skku/index.do)
  | [dudrms33@g.skku.edu](mailto:dudrms33@g.skku.edu)
date: "`r format(Sys.time(), '%d %b, %Y')`"
include-before:
  - \newcommand{\iid}{\stackrel{iid}{\sim}}
  - \newcommand{\indep}{\stackrel{indep}{\sim}}
  - \newcommand{\hsim}{\stackrel{H_0}{\sim}}
  - \newcommand{\ind}{\perp\!\!\!\perp}
  - \newcommand{\R}{\mathbb{R}}
  - $\DeclareMathOperator*{\argmin}{argmin}$
  - $\DeclareMathOperator*{\argmax}{argmax}$
site: bookdown::bookdown_site
documentclass: book
bibliography: [book.bib, packages.bib]
biblio-style: apalike
link-citations: yes
description: "This is a lab session for statistical computing."
---

# Welcome {-}

<img src="cover.png" width="250" height="375" alt="Cover image" align="right" style="margin: 0 1em 0 1em" /></a> Statistical computing mainly treats useful simulation methods.

```{r, eval=FALSE}
library(tidyverse)
```

`tidyverse` package family will be used in every chapter. Loading step is in `_common.R`, so it is not included in the text. Sometimes `data.table` library will be called for efficiency.

## Statistical Computing {-}

We first look at *random generation* methods. Lots of simulation methods are built based on this random numbers.

### Sampling from a fininte population {-}

Generating random numbers is like sampling. From finite population, we can sample data with or without replacement. For example of sampling with replacement, we toss coins 10 times.


```{r}
sample(0:1, size = 10, replace = TRUE)
```

Sampling without replacement: Choose some lottery numbers which consist of 1 to 100.

```{r}
sample(1:100, size = 6, replace = FALSE)
```

### Random generators of common probability distributions {-}

`R` provides some functions which generate random numbers following famous distributions. Although we will learn some skills generating these numbers in basis levels, these functions do the same thing more elegantly.

```{r dbrb, fig.cap="Beta(3,2) random numbers"}
gg_curve(dbeta, from = 0, to = 1, args = list(shape1 = 3, shape2 = 2)) +
  geom_histogram(
    data = tibble(
      rand = rbeta(1000, 3, 2),
      idx = seq(0, 1, length.out = 1000)
    ),
    aes(x = rand, y = ..density..),
    position = "identity",
    bins = 30,
    alpha = .45,
    fill = gg_hcl(1)
  )
```

Figure \@ref(fig:dbrb) shows that `rbeta()` function generate random numbers very well. Histogram is of the random number, and the curve is the true beta distribution.