StatReason

Random Number Generator

Generate a list of random values from a chosen distribution, with a seed that makes the exact sequence fully reproducible, useful for teaching examples, simulations, or spot checks against other software.

What this answers

This calculator answers "how do I generate a list of random values from a named distribution, in a way I can exactly reproduce later?" a common need for teaching examples, simulation inputs, or cross-checking another tool's output.

How it is calculated

Values are drawn using a seeded, fully reproducible pseudorandom generator: uniform values fall anywhere in your chosen range with equal likelihood, normal values follow a bell curve with your chosen mean and standard deviation, integer values simulate a fair die or similar discrete range, and binomial values simulate a fixed number of independent yes/no trials at your chosen probability. The exact same seed and parameters always reproduce the exact same sequence of values.

Worked example

For a uniform distribution between 0 and 1 with a fixed seed, generating 10 values always produces the identical 10 numbers every time you enter that same seed, letting you or anyone else independently reproduce your exact results.

Assumption audit

Calculated from your data: the requested count of pseudo-random values from your chosen distribution and parameters, plus the exact seed used.
Evidence to review: nothing about your own data here; this engine generates values rather than analyzing values you provide.
You must verify: that pseudo-random values are appropriate for your purpose; this generator is not cryptographically secure and should never be used for security-sensitive randomness such as passwords or cryptographic keys.

What this result does not mean

These values are pseudo-random, generated by a deterministic algorithm from a seed, not true physical randomness; for teaching, simulation, and reproducible research examples this distinction rarely matters, but it does matter for any security-sensitive use, which this generator is not intended for.

Common mistakes

Using this generator's output for anything security-sensitive, such as a password, a cryptographic key, or a lottery draw with real money on the line, is the single most important mistake to avoid; this generator's algorithm is designed for speed and statistical quality, not unpredictability against a determined adversary. A second, more minor mistake is expecting a very small generated sample to look perfectly uniform or perfectly bell-shaped; genuine randomness, pseudo or not, always shows some irregularity at small sample sizes.

Limitations

This calculator supports uniform, normal, integer, and binomial distributions only at launch; other named distributions are not available from this specific engine. Output is capped at 10,000 values per generation to keep the page responsive.