Compare Distributions
Math · free browser app
Ten probability distribution families side by side, as density or CDF.
Description
Overlay probability distributions and compare their shapes and moments: normal, uniform, exponential, log-normal, gamma, beta, Student's t, chi-squared, binomial and Poisson. Continuous families draw as curves, discrete ones as points at whole numbers, and every parameter has its own slider.
Switch between the density view (PDF/PMF) and the cumulative view (CDF), where quantiles can be read straight off the curve; a log scale keeps thin tails readable next to tall peaks, and interval probabilities P(a ≤ X ≤ b) appear as shaded area.
Examples
Heavy tails: normal vs. Student's t
Put a normal distribution next to Student's t with ν = 3: same centre, same scale, but the t leaves visibly more probability far from the mean. Flip on the log scale to see how slowly its tails fall — the reason small samples surprise.
The law of rare events: binomial meets Poisson
Set a binomial with n = 50 trials and p = 0.1 next to a Poisson with λ = 5: the two point patterns lie almost on top of each other. Many tries with a small chance each behave like a pure rate.
Reading quantiles: mean is not median
Draw an exponential distribution with rate λ = 1 and switch to the CDF: it crosses 0.5 at x ≈ 0.69 — the median — while the mean sits at 1. In a skewed distribution the two tell different stories.