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

Minimum scale

Required number input.

Shape

Required number input.

Sample count

Required integer input.

Seed

Required string input.

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

Pareto samples

The resulting pareto 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.

• Normal Distribution Box-Muller Sampler

  Generate reproducible normally distributed samples with the Box-Muller transform.

• Beta-Binomial Distribution Sampler

  Generate reproducible beta-binomial samples by drawing a probability from a beta distribution for every experiment.

• Binomial Distribution Sampler

  Generate reproducible binomial random samples.