Berry-Esseen Binomial Jump Distance
Measure the largest normal-approximation error at binomial jumps and compare it with a theorem’s bound.
Free theory articleMeasure the largest normal-approximation error at binomial jumps and compare it with a theorem’s bound.
Concept & interpretation
The Berry-Esseen theorem provides a quantitative bound on the error when approximating the cumulative distribution function (CDF) of a normalized sum of independent random variables with the standard normal CDF. This module focuses on the Binomial distribution, where the theorem gives a universal bound on the maximum approximation error.
Experiment
You can explore this approximation using the interactive module. Follow these steps:
- Open the Berry-Esseen Binomial Jump Distance interactive visualization.
- Select the Trials and Success probability to define the Binomial distribution.
- Choose a Count fraction to select a specific jump point. The module will compute and display the selected error and the maximum Kolmogorov distance across all jumps.
- Observe the visual representation where both exact step CDF and standard normal curve are plotted, showing the exact discrepancies at each jump.