library(ggplot2)
library(gridExtra)
library(patchwork)
library(moments)  # Untuk skewness()

set.seed(123)

n_population <- 10000
populasi <- 15 - rexp(n_population, rate = 0.5)

n_simulasi <- 10000
ukuran_sampel <- 30
rata_rata_sampel <- numeric(n_simulasi)

for (i in 1:n_simulasi) {
  sampel <- sample(populasi, ukuran_sampel, replace = TRUE)
  rata_rata_sampel[i] <- mean(sampel)
}

library(ggplot2)
library(patchwork)
library(grid)

# KURVA DISTRIBUSI MIRING (POPULASI)
x1 <- seq(-3, 2, length.out = 100)
y1 <- dgamma(x1 + 3, shape = 2, scale = 0.5)  # Kurva miring kiri

plot_populasi <- ggplot() +
  geom_area(aes(x = x1, y = y1), 
            fill = "#FF6B8B", alpha = 0.7, color = "#C2185B", size = 1) +
  labs(title = "DISTRIBUSI POPULASI ASLI",
       subtitle = "(Miring / Tidak Beraturan)",
       x = "Nilai",
       y = "Densitas") +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#800000"),
    plot.subtitle = element_text(hjust = 0.5, color = "#666666"),
    panel.grid.minor = element_blank(),
    plot.background = element_rect(fill = "white", color = NA)
  ) +
  scale_x_continuous(limits = c(-3, 3)) +
  annotate("text", x = -1, y = max(y1)*0.8, 
           label = "POPULASI\nMIRING", 
           color = "#800000", fontface = "bold", size = 5)

# KURVA DISTRIBUSI NORMAL (SAMPLING)
x2 <- seq(-3, 3, length.out = 100)
y2 <- dnorm(x2, mean = 0, sd = 0.8)

plot_sampling <- ggplot() +
  geom_area(aes(x = x2, y = y2), 
            fill = "#2196F3", alpha = 0.7, color = "#0D47A1", size = 1) +
  labs(title = "DISTRIBUSI SAMPLING RATA-RATA",
       subtitle = "(Mendekati Distribusi Normal)",
       x = "Rata-rata Sampel",
       y = "Densitas") +
  theme_minimal() +
  theme(
    plot.title = element_text(face = "bold", size = 16, hjust = 0.5, color = "#0D47A1"),
    plot.subtitle = element_text(hjust = 0.5, color = "#666666"),
    panel.grid.minor = element_blank(),
    plot.background = element_rect(fill = "white", color = NA)
  ) +
  scale_x_continuous(limits = c(-3, 3)) +
  annotate("text", x = 0, y = max(y2)*0.8, 
           label = "SAMPLING\nNORMAL", 
           color = "#0D47A1", fontface = "bold", size = 5)

# PLOT DENGAN PANAH TRANSFORMASI
# canvas kosong untuk panah
plot_arrow <- ggplot() +
  annotate("segment", 
           x = 0, xend = 1, y = 0.5, yend = 0.5,
           arrow = arrow(type = "closed", length = unit(0.3, "inches")),
           size = 2, color = "#FF9800") +
  annotate("text", x = 0.5, y = 0.7, 
           label = expression(bold("CLT: n" >= "30")),
           color = "#FF9800", fontface = "bold", size = 6) +
  theme_void() +
  theme(plot.background = element_rect(fill = "white", color = NA))

# 4. LAYOUT FINAL
final_plot <- plot_populasi + plot_arrow + plot_sampling +
  plot_layout(ncol = 3, widths = c(1, 0.3, 1)) +
  plot_annotation(
    title = 'VISUALISASI CENTRAL LIMIT THEOREM',
    subtitle = 'Transformasi dari populasi miring ke distribusi normal melalui sampling',
    caption = 'Asumsi: Ukuran sampel cukup besar (n ≥ 30)',
    theme = theme(
      plot.title = element_text(size = 24, face = "bold", hjust = 0.5, 
                                color = "#800000", margin = margin(t = 10, b = 5)),
      plot.subtitle = element_text(size = 14, hjust = 0.5, 
                                   color = "#444444", margin = margin(b = 15)),
      plot.caption = element_text(size = 12, hjust = 0.5, 
                                  color = "#666666", margin = margin(t = 10)),
      plot.background = element_rect(fill = "white", color = NA),
      plot.margin = margin(20, 20, 20, 20)
    )
  )

print(final_plot)

ggsave("CLT_Visual_Konseptual.png", 
       plot = final_plot, 
       width = 16, 
       height = 8, 
       dpi = 300,
       bg = "white")

library(ggplot2)
library(scales)

set.seed(123)

# Parameter sesuai referensi
p <- 0.10  # p = 0.10
n <- 100   # n = 100
simulasi <- 5000

# Simulasi
data <- data.frame(
  p_hat = rbinom(simulasi, n, p) / n
)

# Hitung proporsi > 0.15
prop_diatas_15 <- mean(data$p_hat > 0.15) * 100

# Visualisasi
ggplot(data, aes(x = p_hat)) +
  # Histogram
  geom_histogram(aes(y = ..density..),
                 bins = 25,
                 fill = "#e3f2fd",
                 color = "#1976d2",
                 alpha = 0.8) +
  
  # Kurva normal
  stat_function(fun = dnorm,
                args = list(mean = p, sd = sqrt(p*(1-p)/n)),
                color = "#1976d2",
                size = 1.2) +
  
  # Garis p = 0.10
  geom_vline(xintercept = p,
             color = "#d32f2f",
             size = 1.5) +
  
  # Area ekor > 0.15
  geom_area(data = subset(data.frame(x = seq(0, 0.25, length.out = 200),
                                     y = dnorm(seq(0, 0.25, length.out = 200), 
                                               mean = p, 
                                               sd = sqrt(p*(1-p)/n))),
                          x > 0.15),
            aes(x = x, y = y),
            fill = "#ffcdd2",
            alpha = 0.6) +
  
  # Garis batas 0.15
  geom_vline(xintercept = 0.15,
             color = "#ff5722",
             size = 1,
             linetype = "dashed") +
  
  # Anotasi minimal
  annotate("text", x = 0.10, y = 15,
           label = "Mean = 0.10",
           color = "#d32f2f",
           size = 4.5,
           fontface = "bold") +
  
  annotate("text", x = 0.18, y = 8,
           label = paste0("Ekor > 0.15\n", round(prop_diatas_15, 1), "%"),
           color = "#ff5722",
           size = 4) +
  
  annotate("text", x = 0.22, y = 12,
           label = expression(paste("n = 100")),
           color = "#1976d2",
           size = 4.5,
           fontface = "bold") +
  
  # Kosmetik
  labs(x = expression(hat(p)), 
       y = "Densitas",
       title = expression(paste("Distribusi Sampling ", hat(p), " (n=100, p=0.10)"))) +
  
  theme_minimal() +
  theme(
    plot.title = element_text(hjust = 0.5, size = 14, face = "bold"),
    panel.grid.minor = element_blank()
  ) +
  
  scale_x_continuous(labels = percent, 
                     limits = c(0, 0.25),
                     breaks = seq(0, 0.25, by = 0.05))