Probabilistic modelling¶

Continuous parametric distributions¶

 Distribution(*args) Base class for probability distributions. Collection. Base class for elliptical distributions. PythonDistribution([dim]) Allow one to override Distribution from Python. Allow one to override Distribution from a chaospy distribution. Allow one 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. Truncated distribution over a mesh. Uniform(*args) Uniform distribution. UniformOverMesh 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. LogNormal distribution parameters. UniformMuSigma(*args) Uniform 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. Merge of a collection of independent distributions. 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. EmpiricalBernstein copula. FarlieGumbelMorgenstern copula. FrankCopula(*args) Frank copula. GumbelCopula(*args) Gumbel copula. IndependentCopula(*args) Independent copula. PlackettCopula(*args) Plackett copula. ExtremeValueCopula(*args) ExtremeValue copula. JoeCopula(*args) Joe copula. GalambosCopula(*args) Galambos copula. MarshallOlkin copula. MaximumEntropyOrderStatisticsCopula copula. MinCopula(*args) MinCopula. NormalCopula(*args) Normal copula. Student 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 one 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 distribution function of a binomial distribution. DistFunc.dHypergeometric(n, k, m, x) The probability distribution function of an hypergeometric distribution. Probability density function of a NonCentralChiSquare distribution. DistFunc.dNonCentralStudent(nu, delta, x) Probability density function of a NonCentralStudent distribution. DistFunc.dNormal(*args) PDF of a unit-variance centered Normal distribution. DistFunc.dPoisson(_lambda, k) probability distribution 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 sample. DistFunc.kFactorPooled(n, m, p, alpha) Exact margin factor for bilateral covering interval of pooled Normal samples. DistFunc.logdBinomial(n, p, k) Logarithm of the probability distribution function of a binomial distribution. DistFunc.logdHypergeometric(n, k, m, x) Logarithm of the probability distribution function of an hypergeometric distribution. Log-PDF of a unit-variance centered Normal distribution. DistFunc.logdPoisson(_lambda, k) Logarithm of the probability distribution function of a Poisson distribution. DistFunc.logpNormal(x[, tail]) Log-CDF of a unit-variance centered Normal distribution. DistFunc.pBeta(p1, p2, x[, tail]) Cumulative distribution function of a Beta distribution on . DistFunc.pDickeyFullerConstant(x[, tail]) Cumulative distribution function of the Dickey-Fuller statistic. DistFunc.pDickeyFullerNoConstant(x[, tail]) Cumulative distribution function of the Dickey-Fuller statistic. DistFunc.pDickeyFullerTrend(x[, tail]) Cumulative distribution function of the Dickey-Fuller statistic. DistFunc.pGamma(k, x[, tail]) Cumulative distribution function of a Gamma distribution on . DistFunc.pHypergeometric(n, k, m, x[, tail]) Cumulative distribution function of an hypergeometric distribution. DistFunc.pKolmogorov(n, x[, tail]) Cumulative distribution function of a Kolmogorov distribution. Cumulative distribution function of a NonCentralChiSquare. DistFunc.pNonCentralStudent(nu, delta, x[, tail]) Cumulative distribution function of a NonCentralStudent distribution. DistFunc.pNormal(*args) Cumulative distribution function of a unit-variance centered Normal distribution. DistFunc.pNormal2D(x1, x2, rho[, tail]) Cumulative distribution function of an 2D standard Normal distribution. DistFunc.pNormal3D(x1, x2, x3, rho12, rho13, ...) Cumulative distribution function of a 3D Normal distribution. DistFunc.pPearsonCorrelation(size, rho[, tail]) Cumulative distribution function of the Pearson statistic distribution. DistFunc.pSpearmanCorrelation(size, rho[, ...]) Cumulative distribution function of a the Spearman correlation distribution. DistFunc.pStudent(*args) Cumulative distribution function of a scalar Student distribution. DistFunc.qBeta(p1, p2, p[, tail]) Quantile of a Beta distribution on . DistFunc.qDickeyFullerConstant(p[, tail]) Quantile of the Dickey-Fuller statistic. DistFunc.qDickeyFullerNoConstant(p[, tail]) Quantile of the Dickey-Fuller statistic. DistFunc.qDickeyFullerTrend(p[, tail]) Quantile of the Dickey-Fuller statistic. DistFunc.qGamma(k, p[, tail]) Quantile of a Gamma distribution on . DistFunc.qNormal(*args) Quantile of a unit-variance centered Normal distribution. DistFunc.qPoisson(_lambda, p[, tail]) Quantile of a Poisson distribution. DistFunc.qStudent(*args) Quantile of a scalar Student distribution. DistFunc.rBeta(*args) Realization of a Beta distribution on . DistFunc.rBinomial(*args) Realization of a binomial distribution. DistFunc.rDiscrete(*args) Realization of a bounded integral discrete distribution. DistFunc.rGamma(*args) Realization of a Gamma distribution on . Realization of an hypergeometric distribution. Realization of a NonCentralChiSquare distribution. Realization of a scalar NonCentralStudent distribution. DistFunc.rNormal(*args) Realization of a unit-variance centered Normal distribution. DistFunc.rPoisson(*args) Realization of a Poisson distribution. DistFunc.rStudent(*args) Realization of a scalar Student distribution. Realization of a uniform distribution over a segment. Realization of a uniform distribution over a triangle. Realization of a uniform distribution over a tetrahedron. Realization of a uniform distribution over a simplex.