# Probabilistic modelling¶

## Continuous parametric distributions¶

 Distribution(*args) Base class for probability distributions. Collection. PythonDistribution([dim]) Allow to override Distribution from Python. Allow to override Distribution from a chaospy distribution. Allow to override Distribution from a scipy distribution.
 Arcsine(*args) Arcsine distribution. Beta(*args) Beta distribution. Burr(*args) Burr distribution. Chi(*args) distribution. ChiSquare(*args) distribution. Dirichlet(*args) Dirichlet distribution. Epanechnikov(*args) Epanechnikov distribution. Exponential(*args) Exponential distribution. FisherSnedecor(*args) Fisher-Snedecor distribution. Frechet(*args) Frechet distribution. Gamma(*args) Gamma distribution. Generalized ExtremeValue distribution. GeneralizedPareto(*args) Generalized Pareto distribution. Gumbel(*args) Gumbel distribution. Histogram(*args) Histogram distribution. InverseChiSquare(*args) InverseChiSquare distribution. InverseGamma(*args) InverseGamma distribution. InverseNormal(*args) Inverse normal distribution. InverseWishart(*args) Inverse-Wishart distribution. KPermutations distribution. Laplace(*args) Laplace distribution. Logistic(*args) Logistic distribution. LogNormal(*args) Lognormal distribution. LogUniform(*args) LogUniform distribution. Meixner distribution. NonCentralChiSquare distribution. NonCentralStudent(*args) NonCentralStudent distribution. Normal(*args) Normal distribution. NormalGamma(*args) NormalGamma distribution. Pareto(*args) Pareto distribution. Rayleigh(*args) Rayleigh distribution. Rice(*args) Rice distribution. SmoothedUniform(*args) SmoothedUniform distribution. SquaredNormal(*args) Squared Normal distribution. Student(*args) Student distribution. Trapezoidal(*args) Trapezoidal distribution. Triangular(*args) Triangular distribution. TruncatedNormal(*args) TruncatedNormal distribution. Uniform(*args) Uniform distribution. VonMises(*args) von Mises distribution. WeibullMin(*args) WeibullMin distribution. WeibullMax(*args) WeibullMax distribution. Wishart(*args) Wishart distribution.

## Discrete parametric distributions¶

 Bernoulli(*args) Bernoulli distribution. Binomial(*args) Binomial distribution. Dirac(*args) Dirac distribution. Geometric(*args) Geometric distribution. Hypergeometric(*args) Hypergeometric distribution. Multinomial(*args) Multinomial distribution. NegativeBinomial(*args) NegativeBinomial distribution. Poisson(*args) Poisson distribution. Skellam(*args) Skellam distribution. UserDefined(*args) UserDefined distribution. ZipfMandelbrot(*args) ZipfMandelbrot distribution.

## Parametrized distributions¶

 Parametrized distribution. Define a distribution with particular parameters. ArcsineMuSigma(*args) Arcsine distribution parameters. BetaMuSigma(*args) Beta distribution parameters. GammaMuSigma(*args) Gamma distribution parameters. GumbelLambdaGamma(*args) Gumbel rate/location parametrization. GumbelMuSigma(*args) Gumbel distribution parameters. LogNormalMuSigma(*args) LogNormal distribution parameters. LogNormal distribution parameters. WeibullMaxMuSigma(*args) WeibullMax distribution parameters. WeibullMinMuSigma(*args) WeibullMin distribution parameters.

## Pseudo-random numbers generator¶

 RandomGenerator(*args, **kwargs) Uniform random generator. Random generator state.

## Combining and transforming distributions¶

 BayesDistribution(*args) Bayes distribution. Composed distribution. Composite distribution. Conditional distribution. Composed distribution. Discrete compound distribution. Maximum distribution. MaximumEntropyOrderStatistics distribution.
 Mixed Histogram/UserDefined distribution. Compatibility tests of marginals with respect to the order statistics constraint. Distribution conditioned by observations.
 Product distribution. RandomMixture(*args) RandomMixture distribution.
 Truncated distribution. KernelMixture(*args) Build a particular linear combination of probability density functions. Mixture(*args) Build a linear combination of probability density functions.

## Copulas¶

Refer to Copulas.

 ArchimedeanCopula(*args) Base class for bivariate Archimedean copulas.
 AliMikhailHaq copula. ClaytonCopula(*args) Clayton copula. FarlieGumbelMorgenstern copula. FrankCopula(*args) Frank copula. GumbelCopula(*args) Gumbel copula. IndependentCopula(*args) Independent copula. PlackettCopula(*args) Plackett copula. EmpiricalBernstein copula. ExtremeValueCopula(*args) ExtremeValue copula. JoeCopula(*args) Joe copula. MarshallOlkin copula. MaximumEntropyOrderStatisticsCopula copula. MinCopula(*args) MinCopula. NormalCopula(*args) Normal copula.

## Combining and transforming copulas¶

 ComposedCopula(*args) Merge of a collection of independent copulas. SklarCopula(*args) Sklar copula. OrdinalSumCopula(*args) Copula built as an ordinal sum of copulas.

## Random vectors¶

 RandomVector(*args) Random vectors. PythonRandomVector([dim]) Allow to overload RandomVector from Python. Random Vector obtained by applying a function. Conditional random vector. Constant Random Vector. UsualRandomVector(*args) Random Vector from a distribution.

## Low-level distribution functions¶

 DistFunc_dBinomial(n, p, k) Probability function of a binomial distribution. DistFunc_dHypergeometric(n, k, m, x) The probability function of an hypergeometric distribution. Probability function of a NonCentralChiSquare distribution. DistFunc_dNonCentralStudent(nu, delta, x) Probability function of a NonCentralStudent distribution. DistFunc_dPoisson(_lambda, k) Probability function of a Poisson distribution. Expectation of the min of n independent standard normal random variables. DistFunc_kFactor(n, p, alpha) Exact margin factor for bilateral covering interval of a Normal population. DistFunc_kFactorPooled(n, m, p, alpha) Exact margin factor for bilateral covering interval of pooled Normal populations. DistFunc_logdBinomial(n, p, k) Logarithm of the probability function of a binomial distribution. DistFunc_logdHypergeometric(n, k, m, x) Logarithm of the probability function of an hypergeometric distribution. DistFunc_logdPoisson(_lambda, k) Logarithm of the probability function of a Poisson distribution. DistFunc_pHypergeometric(n, k, m, x[, tail]) The cumulative probability function of an hypergeometric distribution. DistFunc_pPearsonCorrelation(size, rho[, tail]) Asymptotic probability function for the Pearson correlation. DistFunc_pNormal(\*args) CDF of an unit-variance centered Normal distribution. DistFunc_qNormal(\*args) Quantile of an unit-variance centered Normal distribution. DistFunc_rBinomial(\*args) Realization of a binomial distribution. DistFunc_rDiscrete(\*args) Realization of a bounded integral discrete distribution. Realization of an hypergeometric distribution. DistFunc_rNormal(\*args) Realization of an unit-variance centered Normal distribution. DistFunc_rPoisson(\*args) Realization of a Poisson distribution.