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

mean Direction

Required number input.

concentration

Required number input.

count

Required integer input.

seed

Required string input.

Draw angles in radians on [-π,π) with a circular mean and nonnegative concentration using 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 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.

• Dirichlet Distribution Sampler

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

• Exponential Distribution Sampler

  Draw waiting times using inverse CDF with a positive rate parameter; the mean is 1/rate.

• Multinomial Distribution Sampler

  Draw category-count vectors for a fixed number of independent trials from caller-supplied nonnegative weights, normalized to probabilities.