Statistics

Statistics simulators

Randomness, distributions and the patterns that emerge from them.

Central Limit Theorem

Average samples from any distribution and watch the means pile up into a Gaussian, faster as the sample size grows.

Open simulator

Random Walk

Thousands of aimless walkers spread from a point into a Gaussian whose width grows like the square root of time, the particle view of diffusion.

Open simulator

Joint, Marginals & Conditionals

Every pair of values gets a square whose area is its probability. Drag a box over the table and read the joint, the marginals and a conditional off one selection.

Open simulator

Probability Density

No single value has any probability, only stretches do, so a density is the height whose area is that probability. Drag an interval and read off the integral.

Open simulator

Monte Carlo

Throw random darts at a square with a circle inside and count the hits. The fraction inside estimates π, converging slowly as 1/√n.

Open simulator

Bayes' Theorem

See why a 90% accurate test for a rare disease is usually wrong when it says positive. 1,000 people as dots make the posterior obvious.

Open simulator

Maximum Likelihood

Slide a Gaussian over sample data and watch the likelihood rise and fall. The best fit lands exactly on the sample mean and standard deviation.

Open simulator

Least Squares

Drag data points and fit the best line live. The residuals are drawn as literal squares, least squares minimises their total area.

Open simulator

Wasserstein Distance

Measure the distance between two distributions as the least work to reshape one into the other, the area between their CDFs.

Open simulator