Simulation in R - part 2

Introduction

Simulating data is a powerful way to explore statistical concepts, test hypotheses, or validate models. In this post, you’ll learn how to simulate a continuous variable in R, step by step.

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Step 1: Understanding Continuous Distributions

A continuous variable can take on any value within a range. R provides functions to simulate random numbers from various continuous distributions, such as:

• Normal Distribution (rnorm())
• Uniform Distribution (runif())
• Exponential Distribution (rexp())

In this example, we’ll focus on the normal distribution.

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Step 2: Simulating a Normal Distribution

The normal distribution is characterized by its mean (mean) and standard deviation (sd). Use the rnorm() function to simulate data.

# Parameters for the normal distribution
n <- 1000  # Number of observations
mean <- 50 # Mean of the distribution
sd <- 10   # Standard deviation of the distribution

# Simulating data
set.seed(123)  # Set a seed for reproducibility
simulated_data <- rnorm(n, mean, sd)

# Display the first few simulated values
head(simulated_data)

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Step 3: Visualizing the Simulated Data

Visualizing the data helps ensure it looks as expected. Use a histogram to check the shape of the distribution.

# Load ggplot2 for visualization
library(ggplot2)

# Create a histogram
ggplot(data.frame(x = simulated_data), aes(x)) +
  geom_histogram(binwidth = 2, fill = "blue", alpha = 0.7) +
  labs(title = "Histogram of Simulated Data", x = "Value", y = "Frequency") +
  theme_minimal()

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Step 4: Simulating Other Continuous Distributions

Uniform Distribution

The uniform distribution generates values between a specified minimum and maximum.

# Simulating a uniform distribution
min_val <- 0
max_val <- 100
uniform_data <- runif(n, min_val, max_val)
head(uniform_data)

Exponential Distribution

The exponential distribution is often used to model time between events.

# Simulating an exponential distribution
rate <- 0.1
exponential_data <- rexp(n, rate)
head(exponential_data)

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Conclusion

Simulating continuous variables in R is straightforward and highly versatile. Whether you’re modeling normal, uniform, or exponential data, R’s built-in functions make it easy to generate and explore synthetic datasets.

Try experimenting with different distributions and parameters to see how they influence your data!

What’s Next?

Ready to take your simulations further? Check out the next post in this series:

Next Post

Part 3: Simulating Discrete Distributions in R

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Further Reading

• R Documentation on Random Number Generation
• R for Data Science

Happy coding!