📊 Statistical Distributions

Statistical Distributions — Interactive Probability

Statistical distributions are the mathematical foundation of probability, inference, and data analysis, describing how likely different outcomes are in random experiments. This simulator lets you choose from a library of common distributions — normal, binomial, Poisson, exponential, chi-squared — adjust their parameters, and instantly see how the PDF and CDF shapes change. Computing tail probabilities and confidence intervals directly from the visualization connects theory to practical statistical reasoning.

What you can do in this simulation

• Select a distribution family and adjust parameters to reshape the PDF and CDF curves
• Shade tail regions and compute exact probability values for user-specified intervals
• Overlay multiple distributions on one plot to compare spread and skewness
• Compute mean, variance, skewness, and kurtosis directly from the parameter inputs
• Simulate random samples from the chosen distribution and overlay the empirical histogram

Concepts covered

probability density function · cumulative distribution function · normal distribution · binomial distribution · Poisson distribution · central limit theorem

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Free to use in your browser — no signup required. Found a bug or have an idea to make it better? Tell us.