======================
Probabilistic modeling
======================

.. currentmodule:: openturns

.. _parametric_distributions:

Continuous parametric distributions
===================================

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    Distribution
    DistributionCollection
    EllipticalDistribution
    PythonDistribution
    ChaospyDistribution
    SciPyDistribution

.. autosummary::
    :toctree: _generated/
    :template: Distribution.rst_t

    Arcsine

    :template: classWithPlot.rst_t
    Beta
    Burr

    :template: Distribution.rst_t
    Chi
    ChiSquare

    :template: classWithPlot.rst_t
    Dirichlet

    :template: Distribution.rst_t
    Epanechnikov
    Exponential

    :template: classWithPlot.rst_t
    FisherSnedecor

    :template: Distribution.rst_t
    Frechet

    :template: classWithPlot.rst_t
    Gamma
    GeneralizedExtremeValue
    GeneralizedPareto

    :template: Distribution.rst_t
    Gumbel
    Histogram
    InverseChiSquare
    InverseGamma
    InverseNormal
    InverseWishart
    Laplace
    Logistic
    LogNormal
    LogUniform
    MeixnerDistribution
    NonCentralChiSquare
    NonCentralStudent
    Normal

    :template: classWithPlot.rst_t
    NormalGamma

    :template: Distribution.rst_t
    Pareto
    Rayleigh
    Rice
    SmoothedUniform
    SquaredNormal
    Student
    Trapezoidal
    Triangular
    TruncatedNormal

    :template: classWithPlot.rst_t
    TruncatedOverMesh

    :template: Distribution.rst_t
    Uniform

    :template: classWithPlot.rst_t
    UniformOverMesh
    UniformOrderStatistics
    experimental.MarginalUniformOrderStatistics

    :template: Distribution.rst_t
    VonMises

    :template: classWithPlot.rst_t
    WeibullMin
    WeibullMax

    :template: Distribution.rst_t
    Wishart

Discrete parametric distributions
=================================

.. autosummary::
    :toctree: _generated/
    :template: Distribution.rst_t

    Bernoulli
    Binomial

    :template: classWithPlot.rst_t
    experimental.CombinationsDistribution

    :template: Distribution.rst_t
    Dirac
    FiniteDiscreteDistribution
    Geometric
    Hypergeometric
    Multinomial

    :template: classWithPlot.rst_t
    Polya
    KPermutationsDistribution

    :template: Distribution.rst_t
    Poisson
    Skellam
    ZipfMandelbrot

Parametrized distributions
==========================

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    ParametrizedDistribution
    DistributionParameters
    ArcsineMuSigma
    BetaMuSigma
    GammaMuSigma
    GumbelLambdaGamma
    GumbelMuSigma
    LogNormalMuSigma
    LogNormalMuSigmaOverMu
    LogNormalMuErrorFactor
    UniformMuSigma
    WeibullMaxMuSigma
    WeibullMinMuSigma

Pseudo-random numbers generator
===============================

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    RandomGenerator
    RandomGeneratorState

Combining and transforming distributions
========================================

.. autosummary::
    :toctree: _generated/

    :template: DistributionHighDimension.rst_t
    BlockIndependentDistribution

    :template: classWithPlot.rst_t
    CompositeDistribution

    :template: Distribution.rst_t
    CompoundDistribution
    CumulativeDistributionNetwork
    DiscreteCompoundDistribution

    :template: classWithPlot.rst_t
    JointByConditioningDistribution

    :template: DistributionHighDimension.rst_t
    JointDistribution

    :template: Distribution.rst_t
    KernelMixture
    LinearCombinationDistribution

    :template: class.rst_t
    MarginalDistribution

    :template: Distribution.rst_t
    MaximumDistribution

    :template: classWithPlot.rst_t
    MaximumEntropyOrderStatisticsDistribution

    :template: class.rst_t
    MixedHistogramFiniteDiscreteDistribution

    :template: classWithPlot.rst_t
    Mixture

    :template: class.rst_t
    OrderStatisticsMarginalChecker

    :template: classWithPlot.rst_t
    PointConditionalDistribution

    :template: class.rst_t
    PosteriorDistribution

    :template: Distribution.rst_t
    ProductDistribution
    TruncatedDistribution

.. _copulas:

Copulas
=======

Refer to :ref:`copula`.

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    ArchimedeanCopula

.. autosummary::
    :toctree: _generated/
    :template: Copula.rst_t

    AliMikhailHaqCopula
    ClaytonCopula
    EmpiricalBernsteinCopula
    FarlieGumbelMorgensternCopula
    FrankCopula
    GumbelCopula
    IndependentCopula
    PlackettCopula
    ExtremeValueCopula
    JoeCopula
    GalambosCopula

    :template: classWithPlot.rst_t

    MarshallOlkinCopula

    :template: class.rst_t
    MinCopula

    :template: Copula.rst_t
    NormalCopula
    StudentCopula


Combining and transforming copulas
==================================

.. autosummary::
    :toctree: _generated/
    :template: DistributionHighDimension.rst_t

    BlockIndependentCopula

    :template: Copula.rst_t
    SklarCopula

    :template: classWithPlot.rst_t
    OrdinalSumCopula

Random vectors
==============

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    RandomVector

    :template: classWithPlot.rst_t
    PythonRandomVector
    CompositeRandomVector
    CompoundRandomVector

    :template: class.rst_t
    ConstantRandomVector

    :template: classWithPlot.rst_t
    UsualRandomVector
    experimental.RatioOfUniforms

Markov Chain Monte Carlo (MCMC)
===============================

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    MetropolisHastings
    RandomWalkMetropolisHastings
    IndependentMetropolisHastings
    RandomVectorMetropolisHastings
    Gibbs
    UserDefinedMetropolisHastings

Low-level distribution functions
================================

.. autosummary::
    :toctree: _generated/
    :template: function.rst_t

    DistFunc.dBinomial
    DistFunc.dHypergeometric
    DistFunc.dNonCentralChiSquare
    DistFunc.dNonCentralStudent
    DistFunc.dNormal
    DistFunc.dPoisson
    DistFunc.eZ1
    DistFunc.kFactor
    DistFunc.kFactorPooled
    DistFunc.logdBinomial
    DistFunc.logdHypergeometric
    DistFunc.logdNormal
    DistFunc.logdPoisson
    DistFunc.logpNormal
    DistFunc.pBeta
    DistFunc.pDickeyFullerConstant
    DistFunc.pDickeyFullerNoConstant
    DistFunc.pDickeyFullerTrend
    DistFunc.pGamma
    DistFunc.pHypergeometric
    DistFunc.pKolmogorov
    DistFunc.pNonCentralChiSquare
    DistFunc.pNonCentralStudent
    DistFunc.pNormal
    DistFunc.pNormal2D
    DistFunc.pNormal3D
    DistFunc.pPearsonCorrelation
    DistFunc.pSpearmanCorrelation
    DistFunc.pStudent
    DistFunc.pStudent2D
    DistFunc.qBeta
    DistFunc.qDickeyFullerConstant
    DistFunc.qDickeyFullerNoConstant
    DistFunc.qDickeyFullerTrend
    DistFunc.qGamma
    DistFunc.qNormal
    DistFunc.qPoisson
    DistFunc.qStudent
    DistFunc.rBeta
    DistFunc.rBinomial
    DistFunc.rDiscrete
    DistFunc.rGamma
    DistFunc.rHypergeometric
    DistFunc.rNonCentralChiSquare
    DistFunc.rNonCentralStudent
    DistFunc.rNormal
    DistFunc.rPoisson
    DistFunc.rStudent
    DistFunc.rUniformSegment
    DistFunc.rUniformTriangle
    DistFunc.rUniformTetrahedron
    DistFunc.rUniformSimplex

.. _isoprobabilistic_transformations:

Isoprobabilistic transformation
===============================

Refer to :ref:`isoprobabilistic_transformation`.

.. currentmodule:: openturns

.. autosummary::
    :toctree: _generated/
    :template: class.rst_t

    DistributionTransformation
    MarginalTransformationEvaluation
    MarginalTransformationGradient
    MarginalTransformationHessian
    InverseNatafEllipticalCopulaEvaluation
    InverseNatafEllipticalCopulaGradient
    InverseNatafEllipticalCopulaHessian
    NatafEllipticalCopulaEvaluation
    NatafEllipticalCopulaGradient
    NatafEllipticalCopulaHessian
    InverseNatafIndependentCopulaEvaluation
    InverseNatafIndependentCopulaGradient
    InverseNatafIndependentCopulaHessian
    NatafIndependentCopulaEvaluation
    NatafIndependentCopulaGradient
    NatafIndependentCopulaHessian
    InverseNatafEllipticalDistributionEvaluation
    InverseNatafEllipticalDistributionGradient
    InverseNatafEllipticalDistributionHessian
    NatafEllipticalDistributionEvaluation
    NatafEllipticalDistributionGradient
    NatafEllipticalDistributionHessian
    InverseRosenblattEvaluation
    RosenblattEvaluation
