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

degrees Of Freedom

Required number input.

Sample count

Required integer input.

Seed

Required string input.

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

• F-Distribution Sampler

  Draw an F ratio from two independent chi-square variates, each divided by its degrees of freedom.

• Rejection Sampler

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

• Chi-Square Distribution Sampler

  Sample chi-square variates as gamma(shape=df/2, scale=2) with positive degrees of freedom.