Linked from

The 38 pages that link to Binomial distribution, each with the reason it gives.

• Random variableBroader topic: It models a random variable counting successes across repeated trials.

• Probability distributionBroader topic: It models counts when trials share two outcomes and a constant success chance.

• Binomial coefficientRelated: Its probability formula weights each success count by the corresponding binomial coefficient.

• Binomial theoremRelated: Its probability formula uses binomial coefficients to count success patterns.

• Poisson distributionCompared with: It models bounded trial counts, while Poisson counts are unbounded and often approximate rare successes.

• Independence (probability theory)Related: Its probability formula relies on repeated trials with the same success probability and independence.

• Probability mass functionBroader topic: Its mass function gives the probability of each possible success count.

• Geometric distributionRelated: It counts successes across a fixed horizon, while the geometric distribution counts trials until the first.

• Pascal's triangleRelated: Its probability weights include a row of the triangle as binomial coefficients.

• Bernoulli distributionNarrower topic: It sums independent Bernoulli outcomes when counting successes across repeated trials.

• Bernoulli trialNarrower topic: It describes the success count when identical Bernoulli trials are repeated independently.

• Stirling's approximationRelated: Approximating its factorials gives useful estimates for probabilities and tail behavior.

• Beta distributionRelated: Its unknown success probability is commonly assigned a beta prior.

• Chernoff boundRelated: Chernoff bounds give exponentially small estimates for unusually high or low success counts.

• Method of momentsRelated: Its mean directly relates the success probability to the observed sample average.

• Order statisticRelated: Counting observations below a threshold yields binomial probabilities for an order statistic.

• Jacob BernoulliRelated: It models the success counts whose relative frequencies Bernoulli studied.

• Abraham de MoivreRelated: Its probabilities are central to de Moivre’s normal approximation.

• Beta functionCompared with: Its discrete counting probabilities contrast with beta-function integrals used in Bayesian inference.

• CombinationRelated: Its probability formula counts which trial positions produce the specified number of successes.

• Hypergeometric distributionCompared with: Unlike this model, the binomial distribution does not account for depletion in a finite population.

• Negative binomial distributionCompared with: It fixes the trial count, while the negative binomial fixes the required success count.

• Stars and barsCompared with: It is the two-category case, while stars and bars counts allocations of identical objects.

• Gambler’s ruinRelated: After a fixed number of bets, wins and losses determine the fortune’s displacement.

• Bernoulli's inequalityRelated: Bounds on powers of 1+x help estimate probabilities built from repeated independent trials.

• Vandermonde's identityRelated: Combining independent binomial counts invokes the coefficient identity behind binomial convolution.

• Poisson limit theoremNarrower topic: The theorem starts with this distribution and takes its rare-event limit.

• Binomial (algebra)Compared with: Its name comes from binomial coefficients, but it is a probability model rather than an algebraic expression.

• Pascal's ruleRelated: Its probability formula contains coefficients readily computed by the recurrence.

• Rao–Blackwell theoremRelated: Its sufficient success count can replace individual outcomes when conditioning an estimator.

• Berry–Esseen theoremBroader topic: Its standardized form can be approximated by a normal law, with error bounded using the theorem.

• Condorcet's jury theoremRelated: It models how many voters choose correctly when each votes independently with equal accuracy.

• Lehmann–Scheffé theoremRelated: The success count is complete and sufficient for the success probability in the fixed-trial model.

• De Moivre–Laplace theoremNarrower topic: The theorem approximates this distribution when the trial count grows.

• Le Cam's theoremCompared with: Its classical Poisson approximation is a special case related to the theorem's setting.

• Bienaymé's identityBroader topic: Its variance follows by adding the variances of independent Bernoulli trials.

• Hellin's lawCompared with: It models counts from explicit trial assumptions rather than the law's observed ratios.

• Law of Truly Large NumbersBroader topic: It gives the exact chance of zero or more rare-event occurrences in a fixed set of trials.