Probability Tools

Browse all available probability tools.

Available tools

Bayesian Network Simulator Draw reproducible ancestral samples from a Boolean Bayesian network and estimate its marginals.
Beta Distribution Sampler Generate reproducible beta-distributed values from two independently sampled gamma variates.
Beta-Binomial Distribution Sampler Generate reproducible beta-binomial samples by drawing a probability from a beta distribution for each experiment.
Binomial Distribution Sampler Generate reproducible binomial random samples.
Bivariate Normal Gibbs Sampler Alternate conditional Gaussian draws for a zero-mean, unit-variance bivariate normal with caller-supplied correlation. Samples are autocorrelated.
Cauchy Distribution Sampler Sample a Cauchy distribution by inverse CDF from a seed. Cauchy samples have no finite mean or variance.
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.
Discrete Importance Sampler Draw category indices from a proposal distribution and return target/proposal importance weights; proposal support must cover every positive target category.
Empirical Probability Calculator Calculate empirical probability from observed successes and trials.
Expected Value Calculator Calculate the probability-weighted expected value of discrete outcomes.
Exponential Distribution Sampler Draw waiting times using inverse CDF with a positive rate parameter; the mean is 1/rate.
F-Distribution Sampler Draw an F ratio from two independent chi-square variates, each divided by its degrees of freedom.
Finite-State Markov Chain Monte Carlo Sampler Sample a finite-state Markov chain from a caller-supplied row-stochastic transition matrix and initial state. This samples the chain, not an arbitrary target distribution.
Gamma Distribution Sampler Generate reproducible gamma-distributed samples from a positive shape and scale.
Geometric Distribution Sampler Draw the number of Bernoulli trials until the first success, including the successful trial. Success probability p is in (0,1].
Gumbel Distribution Sampler Draw Gumbel maximum-distribution samples from location and positive scale using inverse CDF.
Hamiltonian Monte Carlo Standard Normal Sampler Run one-dimensional HMC with leapfrog integration and Metropolis correction for the standard normal target; report acceptance rate.
Laplace Distribution Sampler Draw Laplace samples from location and positive scale using the two-sided exponential inverse CDF.
Log-Odds Calculator Calculate natural log-odds from a probability strictly between zero and one.
Lognormal Distribution Sampler Exponentiate a normally distributed variate with log-space mean μ and standard deviation σ; μ is not the arithmetic mean of samples.
Metropolis-Hastings Normal Sampler Use a Gaussian random-walk Metropolis-Hastings chain targeting the standard normal density. Report acceptance rate; samples are correlated.
Multinomial Distribution Sampler Draw category-count vectors for a fixed number of independent trials from caller-supplied nonnegative weights, normalized to probabilities.
Negative Binomial Distribution Sampler Draw the number of failures before a specified integer number of successes in independent Bernoulli trials.
Negative Binomial–Poisson Mixture Sampler Draw a gamma-distributed Poisson rate and then an exact Poisson count; marginal counts follow the negative-binomial gamma-Poisson mixture in the supported rate range.
Normal Distribution Box–Muller Sampler Generate reproducible normally distributed samples with the Box–Muller transform.
Pareto Distribution Sampler Generate reproducible Pareto Type I samples using inverse-transform sampling.
Poisson Distribution Sampler Generate reproducible Poisson-distributed event-count samples.
Poisson–Gamma Mixture Sampler Generate reproducible overdispersed counts by mixing a Poisson rate with a gamma distribution.
Probability Complement Calculator Calculate the complement of a probability.
Rejection Sampler Draw reproducible samples from a standard normal distribution truncated to a selected interval using uniform rejection sampling.
Sequential Monte Carlo Gaussian Filter Run a bootstrap particle filter for a one-dimensional Gaussian random walk observed with Gaussian noise; report weighted posterior means and resampled final particles.
Slice Sampler for Standard Normal Sample the standard normal density with univariate stepping-out and shrinkage slice sampling. Width controls exploration, not the target distribution.
Student T-Distribution Sampler Draw Student-t samples as standard normal divided by the square root of an independent chi-square ratio.
Truncated Dirichlet Process Stick-Breaking Sampler Draw truncated GEM stick-breaking weights from Beta(1, concentration); the final component collects all remaining mass.
Uniform Discrete Distribution Sampler Draw each integer in an inclusive safe-integer range with equal nominal probability using a seeded pseudorandom source.
Von Mises Circular Distribution Sampler Draw angles in radians on [-π,π) with a circular mean and nonnegative concentration using rejection sampling.
Weibull Distribution Sampler Draw nonnegative Weibull variates with positive shape and scale using the inverse CDF.

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