Use this probability or sampling tool to compute a stated quantity or generate reproducible draws from a precisely parameterized distribution or stochastic model.

Mean

Required number input.

Standard deviation

Required number input.

Sample count

Required integer input.

Seed

Required string input.

Generate reproducible normally distributed samples with the Box-Muller transform. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Normal samples

The resulting normal samples returned as a list.

• Results depend on parameterization, support, random source, seed, convergence, burn-in, autocorrelation, proposal quality, normalization, numerical tails, and whether model assumptions match the process. Samples are not exact evidence of convergence.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check analytic moments or known test cases, use independent chains and diagnostics for Monte Carlo methods, report seed and effective sample size, and inspect tail behavior.

• Gamma Distribution Sampler

  Generate reproducible gamma-distributed samples from a positive shape and scale.

• Pareto Distribution Sampler

  Generate reproducible Pareto Type I samples using inverse-transform sampling.

• Poisson Distribution Sampler

  Generate reproducible Poisson-distributed event-count samples.