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

location

Required number input.

scale

Required number input.

Sample count

Required integer input.

Seed

Required string input.

Sample a Cauchy distribution by inverse CDF from a seed. Cauchy samples have no finite mean or variance. 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.

• Exponential Distribution Sampler

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

• Gumbel Distribution Sampler

  Draw Gumbel maximum-distribution samples from location and positive scale using inverse CDF.

• Laplace Distribution Sampler

  Draw Laplace samples from location and positive scale using the two-sided exponential inverse CDF.