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

success Probability

Required number input.

Sample count

Required integer input.

Seed

Required string input.

Draw the number of Bernoulli trials until the first success, including the successful trial. Success probability p is in (0,1]. 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.

• Negative Binomial Distribution Sampler

  Draw the number of failures before a specified integer number of successes in independent Bernoulli trials.

• Multinomial Distribution Sampler

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

• Exponential Distribution Sampler

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