# Parameter distribusi
mu <- 10 # Rata-rata (mean)
sigma <- 2 # Deviasi standar (sd)
# Membuat rentang nilai x dari -4 sampai 4
x <- seq(mu - 4 * sigma, mu + 4 * sigma, length.out = 500)
y <- dnorm(x, mean = mu, sd = sigma)
# Garis kurva utama
plot(x, y, type = "l", col = "pink", lwd = 2.5,
main = "Kurva Distribusi Normal Standar N(0, 1)",
xlab = "Nilai X", ylab = "Densitas",
las = 1, bty = "l")
# Menambahkan garis kisi (grid) dan warna di bawah kurva
grid()
polygon(c(x, rev(x)), c(y, rep(0, length(y))),
col = rgb(0.12, 0.47, 0.71, 0.2), border = NA)
# Parameter
mu <- 10
varian <- 2
sigma <- sqrt(varian) # Deviasi standar = sqrt(2) ≈ 1.414
# Rentang sumbu x (4 deviasi standar di kiri dan kanan mean)
x <- seq(mu - 4 * sigma, mu + 4 * sigma, length.out = 500)
y <- dnorm(x, mean = mu, sd = sigma)
# Plot kurva
plot(x, y, type = "l", col = "pink", lwd = 2.5,
main = expression(paste("Distribusi Normal ", N(mu == 10, sigma^2 == 2))),
xlab = "Nilai X", ylab = "Densitas",
las = 1, bty = "l")
grid()
polygon(c(x, rev(x)), c(y, rep(0, length(y))),
col = rgb(0.12, 0.47, 0.71, 0.2), border = NA)
# Parameter
mu <- 10
var1 <- 1; sd1 <- sqrt(var1)
var2 <- 2; sd2 <- sqrt(var2)
# Rentang sumbu X terfokus di sekitar mu = 10
x <- seq(mu - 4 * sd2, mu + 4 * sd2, length.out = 500)
y1 <- dnorm(x, mean = mu, sd = sd1)
y2 <- dnorm(x, mean = mu, sd = sd2)
# Plot Kurva 1
plot(x, y1, type = "l", col = "#1F77B4", lwd = 2.5,
main = "Kurva Normal Bertumpuk pada Rata-Rata Sama (mu = 10)",
xlab = "Nilai X", ylab = "Densitas",
ylim = c(0, max(y1, y2)), las = 1, bty = "l")
# Area transparan Kurva 1
polygon(c(x, rev(x)), c(y1, rep(0, length(y1))),
col = rgb(0.12, 0.47, 0.71, 0.3), border = NA)
# Tambah Kurva 2
lines(x, y2, col = "#FF7F0E", lwd = 2.5)
# Area transparan Kurva 2
polygon(c(x, rev(x)), c(y2, rep(0, length(y2))),
col = rgb(1.0, 0.5, 0.05, 0.3), border = NA)
grid()
legend("topright",
legend = c(expression(N(10, 1)), expression(N(10, 2))),
col = c("#1F77B4", "#FF7F0E"), lwd = 2.5, bty = "n")
# Parameter Kurva 1
mu1 <- 8; var1 <- 1; sd1 <- sqrt(var1)
# Parameter Kurva 2
mu2 <- 10; var2 <- 2; sd2 <- sqrt(var2)
# Rentang sumbu X mencakup kedua kurva
x <- seq(4, 15, length.out = 500)
y1 <- dnorm(x, mean = mu1, sd = sd1)
y2 <- dnorm(x, mean = mu2, sd = sd2)
# Plot Kurva 1
plot(x, y1, type = "l", col = "#1F77B4", lwd = 2.5,
main = "Kurva Normal Bertumpuk dengan Mean Berbeda",
xlab = "Nilai X", ylab = "Densitas",
ylim = c(0, max(y1, y2)), las = 1, bty = "l")
# Area transparan Kurva 1
polygon(c(x, rev(x)), c(y1, rep(0, length(y1))),
col = rgb(0.12, 0.47, 0.71, 0.3), border = NA)
# Tambah Kurva 2
lines(x, y2, col = "#FF7F0E", lwd = 2.5)
# Area transparan Kurva 2
polygon(c(x, rev(x)), c(y2, rep(0, length(y2))),
col = rgb(1.0, 0.5, 0.05, 0.3), border = NA)
grid()
legend("topright",
legend = c(expression(N(8, 1)), expression(N(10, 2))),
col = c("#1F77B4", "#FF7F0E"), lwd = 2.5, bty = "n")
# Parameter (mu dan sd)
params <- list(
c(mu = 0, sd = 2, col = "blue"), # Biru
c(mu = 2, sd = 1, col = "green"), # Hijau
c(mu = 5, sd = 5, col = "red"), # Merah
c(mu = 10, sd = 3, col = "purple"), # Ungu
c(mu = 1.5, sd = 0.1, col = "orange") # Oranye
)
# Rentang sumbu X
x <- seq(-11, 20, length.out = 2000)
# Plot Kurva 1 sebagai dasar
y1 <- dnorm(x, mean = 0, sd = 2)
plot(x, y1, type = "l", col = "blue", lwd = 2,
main = "Perbandingan 5 Distribusi Normal Bertumpuk",
xlab = "Nilai X", ylab = "Densitas",
ylim = c(0, 4), # Membatasi sumbu Y agar kurva lain tetap terlihat jelas
las = 1, bty = "l")
# Menambahkan kurva sisanya dengan perulangan (loop)
for (p in params) {
m <- as.numeric(p["mu"])
s <- as.numeric(p["sd"])
cl <- p["col"]
y <- dnorm(x, mean = m, sd = s)
lines(x, y, col = cl, lwd = 2)
polygon(c(x, rev(x)), c(y, rep(0, length(y))),
col = adjustcolor(cl, alpha.f = 0.15), border = NA)
}
grid()
legend("topright",
legend = c("N(0, sd=2)", "N(2, sd=1)", "N(5, sd=5)", "N(10, sd=3)", "N(1.5, sd=0.1)"),
col = c("blue", "green", "red", "purple", "orange"),
lwd = 2, bty = "n")
library(ggplot2)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
# 1. Definisikan parameter
dist_info <- data.frame(
label = factor(
c("1. N(0, sd=2)", "2. N(2, sd=1)", "3. N(5, sd=5)", "4. N(10, sd=3)", "5. N(1.5, sd=0.1)"),
levels = c("1. N(0, sd=2)", "2. N(2, sd=1)", "3. N(5, sd=5)", "4. N(10, sd=3)", "5. N(1.5, sd=0.1)")
),
mu = c(0, 2, 5, 10, 1.5),
sd = c(2, 1, 5, 3, 0.1)
)
# 2. Bangkitkan titik-titik data untuk setiap panel
df_plot <- dist_info %>%
rowwise() %>%
do({
x_vals <- seq(.$mu - 4 * .$sd, .$mu + 4 * .$sd, length.out = 300)
y_vals <- dnorm(x_vals, mean = .$mu, sd = .$sd)
data.frame(label = .$label, x = x_vals, y = y_vals)
})
# 3. Plot terpisah dengan facet_wrap
ggplot(df_plot, aes(x = x, y = y, fill = label, color = label)) +
geom_area(alpha = 0.25) +
geom_line(linewidth = 1) +
facet_wrap(~ label, scales = "free", ncol = 3) + # 'scales = free' menyesuaikan sumbu X & Y
labs(title = "Visualisasi Terpisah 5 Distribusi Normal",
x = "Nilai X",
y = "Densitas") +
theme_minimal() +
theme(legend.position = "none",
strip.text = element_text(face = "bold", size = 10))
library(ggplot2)
# Rentang sumbu X
df_plot <- data.frame(x = c(-4, 4))
ggplot(df_plot, aes(x = x)) +
# t-distribution df = 1 (Tebal di ekor / heavy-tailed)
stat_function(fun = dt, args = list(df = 1),
aes(color = "t (df = 1)"), linewidth = 1) +
# t-distribution df = 5
stat_function(fun = dt, args = list(df = 5),
aes(color = "t (df = 5)"), linewidth = 1) +
# t-distribution df = 30
stat_function(fun = dt, args = list(df = 30),
aes(color = "t (df = 30)"), linewidth = 1) +
# Normal Standar N(0,1) sebagai pembanding (Garis Putus-Putus)
stat_function(fun = dnorm, args = list(mean = 0, sd = 1),
aes(color = "Normal Standar N(0,1)"),
linewidth = 1.2, linetype = "dashed") +
# Skala Warna & Legenda
scale_color_manual(name = "Distribusi",
values = c("t (df = 1)" = "#D62728", # Merah
"t (df = 5)" = "#FF7F0E", # Oranye
"t (df = 30)" = "#2CA02C", # Hijau
"Normal Standar N(0,1)" = "#1F77B4")) + # Biru
labs(title = "Perbandingan Simultan Distribusi t-Student & Normal Standar",
subtitle = "Makin besar df, distribusi t makin mendekati Normal Standar",
x = "Nilai t / Z",
y = "Densitas") +
theme_minimal() +
theme(legend.position = "top")
library(ggplot2)
library(dplyr)
# 1. Menyiapkan data untuk masing-masing distribusi
df_norm <- data.frame(dist = "1. Distribusi Normal N(0, 1)", x = seq(-4, 4, length.out = 400)) %>%
mutate(y = dnorm(x, mean = 0, sd = 1))
df_t <- data.frame(dist = "2. Distribusi t-Student (df = 3)", x = seq(-4, 4, length.out = 400)) %>%
mutate(y = dt(x, df = 3))
df_ray <- data.frame(dist = "3. Distribusi Rayleigh R (scale = 2)", x = seq(0, 8, length.out = 400)) %>%
mutate(y = (x / 2^2) * exp(-x^2 / (2 * 2^2)))
df_chisq <- data.frame(dist = "4. Distribusi Chi-Square (df = 4)", x = seq(0, 12, length.out = 400)) %>%
mutate(y = dchisq(x, df = 4))
# 2. Penggabungan data
df_all <- bind_rows(df_norm, df_t, df_ray, df_chisq)
# 3. Plot terpisah dengan facet_wrap (Grid 2x2)
ggplot(df_all, aes(x = x, y = y, fill = dist, color = dist)) +
geom_area(alpha = 0.25) +
geom_line(linewidth = 1) +
facet_wrap(~ dist, scales = "free", ncol = 2) +
scale_color_manual(values = c("#1F77B4", "#FF7F0E", "#2CA02C", "#D62728")) +
scale_fill_manual(values = c("#1F77B4", "#FF7F0E", "#2CA02C", "#D62728")) +
labs(title = "Visualisasi Terpisah 4 Distribusi Statistika",
x = "Nilai X",
y = "Densitas") +
theme_minimal() +
theme(legend.position = "none",
strip.text = element_text(face = "bold", size = 10))
library(ggplot2)
library(dplyr)
# Memuat package 'Actuar' untuk fungsi densitas Pareto jika tersedia,
# atau kita definisikan fungsi PDF Pareto (Type II / Lomax) secara manual:
dpareto_custom <- function(x, shape, scale) {
ifelse(x < 0, 0, (shape / scale) * (1 + x / scale)^(-(shape + 1)))
}
# Fungsi PDF Rayleigh (Distribusi R)
drayleigh_custom <- function(x, scale) {
ifelse(x < 0, 0, (x / scale^2) * exp(-x^2 / (2 * scale^2)))
}
# 1. Menyiapkan data untuk 9 Distribusi
# -------------------------------------------------------------
df_t <- data.frame(dist = "1. t-Student (df = 3)", x = seq(-4, 4, length.out = 300)) %>%
mutate(y = dt(x, df = 3))
df_r <- data.frame(dist = "2. Rayleigh / R (scale = 2)", x = seq(0, 8, length.out = 300)) %>%
mutate(y = drayleigh_custom(x, scale = 2))
df_chisq <- data.frame(dist = "3. Chi-Square (df = 4)", x = seq(0, 14, length.out = 300)) %>%
mutate(y = dchisq(x, df = 4))
df_gamma <- data.frame(dist = "4. Gamma (shape = 2, rate = 1)", x = seq(0, 10, length.out = 300)) %>%
mutate(y = dgamma(x, shape = 2, rate = 1))
df_weibull <- data.frame(dist = "5. Weibull (shape = 1.5, scale = 1)", x = seq(0, 5, length.out = 300)) %>%
mutate(y = dweibull(x, shape = 1.5, scale = 1))
df_exp <- data.frame(dist = "6. Eksponensial (rate = 0.8)", x = seq(0, 6, length.out = 300)) %>%
mutate(y = dexp(x, rate = 0.8))
df_pareto <- data.frame(dist = "7. Pareto (shape = 3, scale = 1)", x = seq(0, 5, length.out = 300)) %>%
mutate(y = dpareto_custom(x, shape = 3, scale = 1))
df_unif <- data.frame(dist = "8. Uniform (min = 0, max = 5)", x = seq(-1, 6, length.out = 500)) %>%
mutate(y = dunif(x, min = 0, max = 5))
# Memerlukan package 'statmod' untuk Inverse Gaussian (dinvgauss)
# Jika belum ada, bisa install.packages("statmod")
if (!requireNamespace("statmod", quietly = TRUE)) install.packages("statmod")
library(statmod)
df_invgauss <- data.frame(dist = "9. Inverse Gaussian (mean = 1, shape = 1)", x = seq(0.01, 4, length.out = 300)) %>%
mutate(y = dinvgauss(x, mean = 1, shape = 1))
# 2. Penggabungan Seluruh Data
# -------------------------------------------------------------
df_all <- bind_rows(df_t, df_r, df_chisq, df_gamma, df_weibull,
df_exp, df_pareto, df_unif, df_invgauss)
# Menjaga urutan panel sesuai angka
df_all$dist <- factor(df_all$dist, levels = unique(df_all$dist))
# 3. Plot Grid 3x3 Terpisah
# -------------------------------------------------------------
ggplot(df_all, aes(x = x, y = y, fill = dist, color = dist)) +
geom_area(alpha = 0.25) +
geom_line(linewidth = 0.9) +
facet_wrap(~ dist, scales = "free", ncol = 3) +
labs(title = "Visualisasi Terpisah 9 Distribusi Probabilitas Kontinu",
subtitle = "Skala sumbu X dan Y disesuaikan independen di setiap panel",
x = "Nilai X",
y = "Densitas") +
theme_minimal() +
theme(
legend.position = "none",
strip.text = element_text(face = "bold", size = 9),
panel.grid.minor = element_blank()
)
library(ggplot2)
library(dplyr)
if (!requireNamespace("statmod", quietly = TRUE)) install.packages("statmod")
library(statmod)
# Fungsi PDF Rayleigh & Pareto
drayleigh_custom <- function(x, scale) {
ifelse(x < 0, 0, (x / scale^2) * exp(-x^2 / (2 * scale^2)))
}
dpareto_custom <- function(x, shape, scale) {
ifelse(x < 0, 0, (shape / scale) * (1 + x / scale)^(-(shape + 1)))
}
# 1. Menyiapkan Grid X Seragam [-4, 8] untuk Semua Distribusi
# -------------------------------------------------------------
x_grid <- seq(-4, 8, length.out = 500)
df_all_stacked <- bind_rows(
data.frame(dist = "t-Student (df = 3)", x = x_grid, y = dt(x_grid, df = 3)),
data.frame(dist = "Rayleigh (scale = 2)", x = x_grid, y = drayleigh_custom(x_grid, scale = 2)),
data.frame(dist = "Chi-Square (df = 4)", x = x_grid, y = dchisq(x_grid, df = 4)),
data.frame(dist = "Gamma (shape = 2, rate = 1)", x = x_grid, y = dgamma(x_grid, shape = 2, rate = 1)),
data.frame(dist = "Weibull (shape = 1.5, scale = 1)", x = x_grid, y = dweibull(x_grid, shape = 1.5, scale = 1)),
data.frame(dist = "Eksponensial (rate = 0.8)", x = x_grid, y = dexp(x_grid, rate = 0.8)),
data.frame(dist = "Pareto (shape = 3, scale = 1)", x = x_grid, y = dpareto_custom(x_grid, shape = 3, scale = 1)),
data.frame(dist = "Uniform (min = 0, max = 5)", x = x_grid, y = dunif(x_grid, min = 0, max = 5)),
data.frame(dist = "Inverse Gaussian (mean = 1, shape = 1)", x = x_grid, y = ifelse(x_grid <= 0, 0, dinvgauss(x_grid, mean = 1, shape = 1)))
)
# 2. Plot Menumpuk (Overlay)
# -------------------------------------------------------------
ggplot(df_all_stacked, aes(x = x, y = y, color = dist, fill = dist)) +
geom_area(alpha = 0.12, position = "identity") +
geom_line(linewidth = 0.95) +
scale_x_continuous(breaks = seq(-4, 8, by = 2)) +
coord_cartesian(ylim = c(0, 0.8)) +
labs(
title = "Perbandingan Menumpuk 9 Distribusi Probabilitas Kontinu",
subtitle = "Diplot pada rentang sumbu X (-4 hingga 8) dan skala Y yang sama",
x = "Nilai X",
y = "Densitas",
color = "Jenis Distribusi",
fill = "Jenis Distribusi"
) +
theme_minimal() +
theme(
legend.position = "right",
legend.title = element_text(face = "bold", size = 10),
legend.text = element_text(size = 8.5),
plot.title = element_text(face = "bold", size = 13),
panel.grid.minor = element_blank()
)
