In almost every area where probability and statistics are used there have been found a few parametric distribution families that are known to be good models. The origins vary from combinatorial arguments, such as in urn models, to transformations of existing distributions, to different kinds of limit processes. The collection of parametric distributions in the Wolfram Language has been selected in order to provide complete modeling frameworks for a variety of areas. The result is the most extensive collection of parametric distributions ever assembled. From a distribution there are dozens of properties, such as distribution functions, moments, or quantiles, that are directly accessible. Parametric distributions are used as arguments to higher-level functions that compute probabilities, expectations, random variates, or parameter estimates from data. Distributions with undetermined parameters can be used throughout, and later the parameters can be solved for or optimized over, etc.

Discrete Univariate Distributions »

BernoulliDistribution  ▪  BinomialDistribution  ▪  PoissonDistribution  ▪  ...

Normal-Related Distributions »

NormalDistribution  ▪  StudentTDistribution  ▪  LogNormalDistribution  ▪  ...

Exponential-Related Distributions »

ExponentialDistribution  ▪  ErlangDistribution  ▪  LogisticDistribution  ▪  ...

Bounded Domain Distributions »

BetaDistribution  ▪  BinomialDistribution  ▪  UniformDistribution  ▪  ...

Extreme Value Distributions »

GumbelDistribution  ▪  FrechetDistribution  ▪  WeibullDistribution  ▪  ...

Heavy Tail Distributions »

ParetoDistribution  ▪  StableDistribution  ▪  LevyDistribution  ▪  ...

Quantile-Based Distributions

TukeyLambdaDistribution  ▪  WakebyDistribution

Systems of Distributions

JohnsonDistribution  ▪  PearsonDistribution

Multivariate Continuous Distributions

UniformDistribution  ▪  BinormalDistribution  ▪  MultinormalDistribution  ▪  MultivariateTDistribution  ▪  DirichletDistribution  ▪  CopulaDistribution

Multivariate Discrete Distributions

DiscreteUniformDistribution  ▪  MultinomialDistribution  ▪  MultivariateHypergeometricDistribution  ▪  NegativeMultinomialDistribution  ▪  MultivariatePoissonDistribution  ▪  CopulaDistribution