중심극한정리

---

---
class: middle, center

# 정규분포에서 추출한 표본의 평균
## 정규분포(평균 0, 표준편차 1) &rarr; 
### 관측점 50번씩 추출을 100회 반복

---

```r
tibble(var = rnorm(50, mean = 0, sd = 1)) %>%
  ggplot() +
    aes(x = var) +
    geom_rug() +
    geom_histogram(alpha = .15) +
    clt_theme +
    geom_rug(data = . %>%
               summarise(mean_var = mean(var)),
             mapping = aes(x = mean_var),
             color = "goldenrod",
             size = 2) +
    scale_y_continuous(limits = c(0,12)) +
    scale_x_continuous(limits = c(-3.5,3.5))  +
    labs(x = "변수", y = "빈도수",
         title = "정규분포에서 표본 50개 추출",
         subtitle = "정규분포 ~ 평균: 0, 표준편차 = 1")
```
]
 
.panel2-rnorm-10[
![](distribution_clt_files/figure-html/rnorm_10_01_output-1.png)
]

---
count: false
 
### N(0,1) ~ 관측점 50 개 추출
.panel1-rnorm-10[

---

```r
tibble(trial = 1:100) %>%
  crossing(unit_id = 1:50) %>%
  group_by(trial) %>%
  mutate(var = rnorm(1:50, mean = 0, sd = 1)) %>%
  summarise(sample_mean = mean(var)) %>%
  ggplot() +
  aes(x = sample_mean) +
  geom_rug(color = "goldenrod",
           alpha = .2) +
  geom_histogram(alpha = .6,
                 fill = "goldenrod", aes(y = ..density..)
                 ) +
  geom_density(color = "grey") +
  clt_theme +
  scale_x_continuous(limits = c(-3.5, 3.5)) +
    labs(x = "표본 평균", y = "밀도(density)",
         title = "표본평균의 분포")
```
]
 
.panel2-rnorm_sample-1[
![](distribution_clt_files/figure-html/rnorm_sample_1_01_output-1.png)
]

---
class: middle, center

# 균등분포에서 추출한 표본의 평균
## 균등분포(최소 0, 최대 1) &rarr; 
### 관측점 50번씩 추출을 100회 반복

---

```r
tibble(var = runif(50, min = 0, max = 1)) %>%
  ggplot() +
    aes(x = var) +
    geom_rug() +
    geom_histogram(alpha = .15) +
    clt_theme +
    geom_rug(data = . %>%
               summarise(mean_var = mean(var)),
             mapping = aes(x = mean_var),
             color = "goldenrod",
             size = 2) +
    scale_y_continuous(limits = c(0,12)) +
    scale_x_continuous(limits = c(-0.1, 1.1))  +
    labs(x = "변수", y = "빈도수",
         title = "균등분포에서 표본 50개 추출",
         subtitle = "균등분포 ~ 최소: 0, 최대 = 1")
```
]
 
.panel2-runif-10[
![](distribution_clt_files/figure-html/runif_10_01_output-1.png)
]

---
count: false
 
### U(0,1) ~ 관측점 50 개 추출
.panel1-runif-10[

---

```r
tibble(trial = 1:100) %>%
  crossing(unit_id = 1:50) %>%
  group_by(trial) %>%
  mutate(var = runif(1:50, min = 0, max = 1)) %>%
  summarise(sample_mean = mean(var)) %>%
  ggplot() +
  aes(x = sample_mean) +
  geom_rug(color = "goldenrod",
           alpha = .2) +
  geom_histogram(alpha = .6,
                 fill = "goldenrod", aes(y = ..density..)
                 ) +
  geom_density(color = "grey") +
  clt_theme +
  scale_x_continuous(limits = c(-.05,1.05)) +
    labs(x = "표본 평균", y = "밀도(density)",
         title = "표본평균의 분포")
```
]
 
.panel2-runif_sample-1[
![](distribution_clt_files/figure-html/runif_sample_1_01_output-1.png)
]

---
class: middle, center

# 지수분포에서 추출한 표본의 평균
## 지수분포 (λ=1) &rarr; 
### 관측점 50번씩 추출을 100회 반복

---
### 지수분포

```r
lambda <- seq(from = 1, to = 12, by = 1)

lambda_g <- tibble(lambda = lambda) %>% 
  mutate(samples = map(lambda, rexp, n = 50)) %>% 
  unnest(cols = samples) %>% 
  mutate(lamdba = glue::glue("λ = {lambda}")) %>% 
  ggplot(aes(x = samples)) +
    geom_rug(color = "goldenrod",
             alpha = .2) +
    geom_histogram(alpha = .6,
                   fill = "goldenrod", aes(y = ..density..)
                   ) +
    geom_density(color = "grey") +
    clt_theme  +
    facet_wrap( ~ lambda) +
    scale_x_continuous(limits = c(0, 3))
```
]

```r
lambda_g
```

![](distribution_clt_files/figure-html/unnamed-chunk-3-1.png)
]

---

```r
tibble(var = rexp(50, rate = 12)) %>%
  ggplot() +
    aes(x = var) +
    geom_rug() +
    geom_histogram(alpha = .15) +
    clt_theme +
    geom_rug(data = . %>%
               summarise(mean_var = mean(var)),
             mapping = aes(x = mean_var),
             color = "goldenrod",
             size = 2) +
    scale_y_continuous(limits = c(0,12)) +
    scale_x_continuous(limits = c(0, 1))  +
    labs(x = "변수", y = "빈도수",
         title = "지수분포에서 표본 50개 추출",
         subtitle = "지수분포 ~ λ = 12")
```
]
 
.panel2-rexp-10[
![](distribution_clt_files/figure-html/rexp_10_01_output-1.png)
]

---
count: false
 
### Exp(12) ~ 관측점 50 개 추출
.panel1-rexp-10[

---

```r
tibble(trial = 1:100) %>%
  crossing(unit_id = 1:50) %>%
  group_by(trial) %>%
  mutate(var = rexp(1:50, rate = 12)) %>%
  summarise(sample_mean = mean(var)) %>%
  ggplot() +
  aes(x = sample_mean) +
  geom_rug(color = "goldenrod",
           alpha = .2) +
  geom_histogram(alpha = .6,
                 fill = "goldenrod", aes(y = ..density..)
                 ) +
  geom_density(color = "grey") +
  clt_theme +
  scale_x_continuous(limits = c(0, 0.3)) +
    labs(x = "표본 평균", y = "밀도(density)",
         title = "표본평균의 분포")
```
]
 
.panel2-rexp_sample-1[
![](distribution_clt_files/figure-html/rexp_sample_1_01_output-1.png)
]