At each of 10 different x-values, visualize how √n·(F̂ₙ(x) - F(x)) / √[F(x)·(1-F(x))] converges to N(0,1).
Each x-position shows 5 overlapping histograms (colored by sample size n) plus the theoretical normal curve in cyan.
🎯 What to Look For:
Convergence Pattern: As n increases (red → blue), histograms get closer to the cyan normal curve
Variance Effect: Middle quantiles (F(x) ≈ 0.5) have maximum variance, extreme quantiles have less
Universal Shape: Despite different distributions, all standardized ECDFs converge to the same N(0,1)
Sample Size Impact: Larger n = tighter distribution = better approximation to true CDF
This visualization samples 10 different x-values across the distribution's support. At each x-value (positioned along the horizontal axis):
We run many simulations for each sample size n
For each simulation, we compute Zₙ(x) - the standardized deviation from the true CDF
The histograms show the empirical distribution of Zₙ(x), all centered at 0
As n increases, the distributions tighten and converge to N(0,1) (cyan curve)
Key observations: The variance F(x)·(1-F(x)) is maximized when F(x) = 0.5 (median),
so convergence may appear different at different quantiles even though all are standardized to have variance 1.