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

Sample count

Required integer input.

Minimum

Required number input.

Maximum

Required number input.

Seed

Required string input.

Draw reproducible standard-normal samples truncated to an interval using uniform rejection 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]

Samples

The resulting 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.

• Student T-Distribution Sampler

  Draw Student-t samples as standard normal divided by the square root of an independent chi-square ratio.

• Metropolis-Hastings Normal Sampler

  Use a Gaussian random-walk Metropolis-Hastings chain targeting the standard normal density. Report acceptance rate; samples are correlated.

• Normal Distribution Box-Muller Sampler

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