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

Alpha

Required number input.

Beta

Required number input.

Samples

Required integer input.

Seed

Required string input.

Generate reproducible beta-distributed values from two gamma variates. 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]

Beta samples

The resulting beta samples returned as an object.

• 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.

• Beta-Binomial Distribution Sampler

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

• Normal Distribution Box-Muller Sampler

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