Probability Tools
Browse all available probability tools.
Available tools
- Atom Probability Lower Slack Tool Calculate atom probability lower slack from explicit caller-supplied inputs.
- Bayes Likelihood Zero Evidence Flag Tool Binary Bayes update with impossible evidence flagged and a zero posterior placeholder.
- Bayesian Network Simulator Draw reproducible ancestral samples from a Boolean Bayesian network and estimate its marginals.
- Bernoulli Fisher Information One Point Tool Calculate bernoulli fisher information one point from explicit caller-supplied inputs.
- Bernoulli Log Likelihood Trial Tool Return one finite Bernoulli log-likelihood term. An impossible observation is rejected because its negative-infinite log-likelihood is not portable JSON.
- Bernoulli Logit Hessian Term Tool Return the log-likelihood Hessian with respect to a Bernoulli logit at a supplied probability.
- Bernoulli Observed Information One Trial Tool Compute bernoulli observed information one trial from explicit bounded inputs.
- Bernoulli Trial Signed Residual Subtract an explicit predicted Bernoulli success probability from a supplied zero-or-one observation.
- Beta Density Endpoint Power Test Tool Classify the Beta density at zero from its positive first shape parameter, holding the second shape positive.
- 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.
- Binary Observation Log Likelihood Ratio Term Tool Compute binary observation log likelihood ratio term from explicit bounded inputs.
- Binomial Distribution Sampler Generate reproducible binomial random samples.
- Binomial Mass Mode Tie Boundary Tool Calculate binomial mass mode tie boundary from explicit caller-supplied inputs.
- Bivariate Normal Gibbs Sampler Alternate conditional Gaussian draws for a zero-mean, unit-variance bivariate normal with caller-supplied correlation. Samples are autocorrelated.
- Categorical Atom Odds Factor Tool Compute one atom’s normalized probability and odds from supplied nonnegative categorical masses.
- Categorical Label Probability Lookup Look up exact label text in an explicit unique-label probability table, using a false flag and zero sentinel for an absent label.
- Categorical Resampling One Bin Boundary Tool Compute categorical resampling one bin boundary from explicit bounded inputs.
- Cauchy Distribution Sampler Sample a Cauchy distribution by inverse CDF from a seed. Cauchy samples have no finite mean or variance.
- Censored Event Boundary Mass Tool Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.
- Chi-Square Distribution Sampler Sample chi-square variates as gamma(shape=df/2, scale=2) with positive degrees of freedom.
- Conditional Event Complement Gap Tool Calculate conditional event complement gap from explicit caller-supplied inputs.
- Conditional Independence One Cell Residual Tool Compute conditional independence one cell residual from explicit bounded inputs.
- Conditional Odds Joint Cell Crosswalk Tool Calculate conditional odds joint cell crosswalk from explicit caller-supplied inputs.
- Conditional Probability Denominator Check Tool Return P(A and B)/P(B), requiring a positive conditioning probability and a compatible joint probability.
- Conditional Probability Mixture One Component Tool Calculate conditional probability mixture one component from explicit caller-supplied inputs.
- Conditional Probability Zero Case Label Tool Calculate conditional probability zero case label from explicit caller-supplied inputs.
- Dirichlet Distribution Sampler Draw simplex-valued vectors by normalizing independent gamma variates with positive concentration parameters.
- Discrete Cdf Inverse Flat Step Policy Tool Compute discrete cdf inverse flat step policy from explicit bounded inputs.
- Discrete Importance Sampler Draw category indices from a proposal distribution and return target/proposal importance weights; proposal support must cover every positive target category.
- Discrete Tail Endpoint Inclusion Term Tool Calculate discrete tail endpoint inclusion term from explicit caller-supplied inputs.
- Empirical Probability Calculator Calculate empirical probability from observed successes and trials.
- Event Independence Product Bound Gap Tool Calculate event independence product bound gap from explicit caller-supplied inputs.
- Event Indicator Missingness Label Tool Keep missing observation status separate from the binary event indicator; the event flag is ignored when unobserved.
- Event Odds Complement Factor Tool Calculate event odds complement factor from explicit caller-supplied inputs.
- Event Union Disjointness Correction Tool Compute event union disjointness correction from explicit bounded inputs.
- 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 Event Disjoint Union Membership Flag Tool Calculate finite event disjoint union membership flag from explicit caller-supplied inputs.
- Finite Event Mass Remaining Budget Subtract explicitly disjoint assigned probability masses from one without inferring disjointness.
- Finite Support Mass Residual Tool Audit supplied candidate finite-support masses without silently normalizing an invalid total.
- 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.
- Gaussian Mixture Model Sampler Draw labeled samples from supplied univariate Gaussian components using the weighted-item and Box–Muller cores, with scaled weights and the normal core's epsilon-clipped zero-draw convention; no model fitting.
- Geometric Distribution Sampler Draw the number of Bernoulli trials until the first success, including the successful trial. Success probability p is in (0,1].
- Geometric Tail Ratio Tool Return geometric survival-tail ratio (1-p)^k with the k=0 empty-product convention.
- 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.
- Hazard To Discrete Event One Interval Tool Calculate hazard to discrete event one interval from explicit caller-supplied inputs.
- Hypergeometric Adjacent Mass Ratio Tool Calculate hypergeometric adjacent mass ratio from explicit caller-supplied inputs.
- Hypergeometric Support Endpoint Budget Tool Calculate hypergeometric support endpoint budget from explicit caller-supplied inputs.
- Independent Complement Product Two Events Calculate neither and at-least-one probabilities from explicit independent event probabilities.
- Independent Event Xor Probability Tool Calculate independent event xor probability from explicit caller-supplied inputs.
- Joint Probability Rounding Feasibility Tool Compute joint probability rounding feasibility from explicit bounded inputs.
- Laplace Distribution Sampler Draw Laplace samples from location and positive scale using the two-sided exponential inverse CDF.
- Likelihood Impossible Support Flag Compare explicit likelihood magnitude and supplied support membership without treating a density as a bounded probability.
- Likelihood Ratio Explicit Scale Invariance Tool Calculate likelihood ratio explicit scale invariance from explicit caller-supplied inputs.
- Log Probability Logsum Two Weights Tool Compute log probability logsum two weights from explicit bounded inputs.
- Log Probability Weight Centering Offset Tool Calculate log probability weight centering offset from explicit caller-supplied inputs.
- Log-Odds Calculator Calculate natural log-odds from a probability strictly between zero and one.
- Log-Odds Practice Create reproducible practice for Log-Odds Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- 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.
- Mixture Responsibility One Component Tool Calculate mixture responsibility one component from explicit caller-supplied inputs.
- 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 Density Log Ratio Two Points Tool Calculate normal density log ratio two points from explicit caller-supplied inputs.
- Normal Distribution Box–Muller Sampler Generate reproducible normally distributed samples with the Box–Muller transform.
- Odds Product Evidence Factor Tool Multiply supplied sequential conditional likelihood ratios; independence is required if ratios were instead computed marginally.
- Oddsratio Symmetric Table Cell Factor Tool Calculate oddsratio symmetric table cell factor from explicit caller-supplied inputs.
- Pareto Distribution Sampler Generate reproducible Pareto Type I samples using inverse-transform sampling.
- Poisson Distribution Sampler Generate reproducible Poisson-distributed event-count samples.
- Poisson Log Likelihood Count Increment Tool Calculate poisson log likelihood count increment from explicit caller-supplied inputs.
- Poisson–Gamma Mixture Sampler Generate reproducible overdispersed counts by mixing a Poisson rate with a gamma distribution.
- Probability Bound Complement Open Closed Tool Compute probability bound complement open closed from explicit bounded inputs.
- Probability Complement Calculator Calculate the complement of a probability.
- Probability Complement Practice Create reproducible practice for Probability Complement Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Probability Interval Rounding Overlap Check closed overlap of two explicitly supplied probability intervals; disjoint intersections retain inverted bounds and a false flag.
- Probability Partition Exhaustion Residual Tool Calculate probability partition exhaustion residual from explicit caller-supplied inputs.
- Probability: Discrete Cdf Jump Size Tool Recover a discrete atom probability from one supplied left limit and right-continuous CDF value, enforcing monotonic probability bounds.
- Probability: Event Complement Interval Bounds Tool Transform a closed probability-uncertainty interval through the decreasing complement map, reversing endpoints.
- Probability: Finite Support Endpoint Mass Tool Extract endpoint atoms from an explicitly sorted finite probability distribution; duplicate/unsorted support and nonnormalized masses are rejected.
- Probability: Joint Outcome Single Rectangle Mass Tool Recover P(xLower<X<=xUpper,yLower<Y<=yUpper) from four explicitly established joint CDF corner values using rectangle inclusion-exclusion; no distribution fitting.
- Probability: Probability Odds Boundary Policy Tool Report exact probability-to-odds endpoint status without non-JSON infinity; odds zero is unused when finite=false, unlike a clipped probability.
- Probability: Probability Product Log Under Flow Check Tool Multiply supplied probabilities through log space and distinguish true zero factors from floating-point underflow; logProduct zero is unused when zeroFactor=true.
- Probability: Two Event Frechet Bound Interval Tool Return the sharp Frechet bounds on a two-event intersection from its marginals, with no independence assumption.
- Probability: Two Hypothesis Likelihood Weight Normalizer Tool Normalize two nonnegative hypothesis likelihood weights against a supplied binary prior, rejecting zero evidence; likelihoods may be densities above one.
- Rare Event Probability Expm1 Crosswalk Tool Compute rare event probability expm1 crosswalk from explicit bounded inputs.
- 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.
- Truncated Discrete Mass Renormalization Term Tool Calculate truncated discrete mass renormalization term from explicit caller-supplied inputs.
- Two Cdf Values Monotonicity Residual Compare explicit CDF values at strictly ordered arguments without establishing that a complete distribution is valid.
- Two Conditionals Bayes Odds Factor Tool Compute two conditionals bayes odds factor from explicit bounded inputs.
- 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.