Simulation Studies

Simulation studies are crucial for understanding the behavior of statistical methods. Here’s an example of simulating the Central Limit Theorem.

Step 1: Set Parameters

rCopy code# Set parameters
n <- 30  # Sample size
num_simulations <- 1000  # Number of simulations

# Set seed for reproducibility
set.seed(123)

Step 2: Simulate Sample Means

rCopy code# Simulate sample means from an exponential distribution
sample_means <- replicate(num_simulations, mean(rexp(n, rate = 1)))

# View the first few sample means
head(sample_means)

Step 3: Plot the Distribution of Sample Means

rCopy code# Plot the distribution of sample means
hist(sample_means, breaks = 30, main = "Distribution of Sample Means",
     xlab = "Sample Mean", col = "lightblue", probability = TRUE)
lines(density(sample_means), col = "red")