Simulating and Visualising the Central Limit Theorem
9 days ago
- #Statistics
- #R Programming
- #Central Limit Theorem
- The Central Limit Theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases, given certain assumptions.
- Assumptions for the classic CLT include independent and identically distributed (i.i.d) samples, finite mean and variance, and no autocorrelation.
- Simulation in R demonstrates the CLT by sampling from various distributions (uniform, normal, binomial, beta, exponential, chi-square) and observing the convergence of sample means to normality.
- Standardizing sample means using population parameters (mean and standard deviation) helps visualize the convergence to a standard normal distribution.
- In practice, small sample sizes may require using the t-distribution instead of the normal distribution for accurate confidence intervals.
- Skewed distributions (e.g., exponential, chi-square) require larger sample sizes for the CLT to effectively normalize the distribution of sample means.
- Visualizations, including histograms and Q-Q plots, effectively illustrate the convergence of sample means to normality across different distributions and sample sizes.