library(tibble)

set.seed(123)
n <- 1000
mu <- 0
sigma <- 1
df <- tibble(x = rnorm(n, mean = mu, sd = sigma))

gg <- ggplot(df, aes(x = x)) +
  geom_histogram(aes(y = ..density..), bins = 30, fill = "lightblue", color = "black", alpha = 0.6) +
  geom_density(color = "red", size = 1) +
  stat_function(fun = dnorm, args = list(mean = mu, sd = sigma), color = "blue", linetype = "dashed", size = 1) +
  labs(
    title = "Simulated Normal Distribution",
    subtitle = paste0("n = ", n, ", mu = ", mu, ", sigma = ", sigma),
    x = "x",
    y = "Density"
  ) +
  theme_minimal()
gg

import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

def plot_normal_sim(n=1000, mu=0.0, sigma=1.0, bins=30, seed=123):
    rng = np.random.default_rng(seed)
    x = rng.normal(loc=mu, scale=sigma, size=n)
    fig, ax = plt.subplots(figsize=(8, 5))
    sns.histplot(x, bins=bins, stat="density", color="lightblue", edgecolor="black", alpha=0.6, ax=ax)
    sns.kdeplot(x, color="red", linewidth=1.5, ax=ax)
    xs = np.linspace(x.min() - 1, x.max() + 1, 400)
    pdf = (1.0 / (sigma * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((xs - mu) / sigma) ** 2)
    ax.plot(xs, pdf, color="blue", linestyle="--", linewidth=1.5)
    ax.set_title(f"Simulated Normal Distribution\nn={n}, mu={mu}, sigma={sigma}")
    ax.set_xlabel("x")
    ax.set_ylabel("Density")
    fig.tight_layout()
    return fig
plot_normal_sim()

set obs 1000
gen x = rnormal()
twoway (histogram x, fcolor(ltblue) lcolor(black)) (kdensity x, lcolor(red)) (function y=normalden(x), range(-4 4) lcolor(blue) lpattern(dash)), title("Simulated Normal Distribution") subtitle("n=1000, mu=0, sigma=1") legend(off)
graph export "img/pres-symp-jun26/stata_histogram.png", replace