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

numerator Degrees Of Freedom

Required number input.

denominator Degrees Of Freedom

Required number input.

Sample count

Required integer input.

Seed

Required string input.

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

• Student T-Distribution Sampler

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

• Chi-Square Distribution Sampler

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

• Dirichlet Distribution Sampler

  Draw simplex-valued vectors by normalizing independent gamma variates with positive concentration parameters.