Distributions and dependence#

Specify marginals and dependence, and construct probability transformations.

Public entry points#

Object	Purpose
`Normal`	Specify a normal marginal by mean and standard deviation.
`ScipyDist`	Wrap a parameterized SciPy distribution.
`JointDistribution`	Combine marginals with an explicit copula.
`GaussianCopula`	Specify Gaussian dependence.
`StudentTCopula`	Specify Student-t dependence and degrees of freedom.
`FrankCopula`	Specify bivariate Frank dependence.

Use it: Copulas and isoprobabilistic transformations · Dependence and probability transformations · Probability transformations and copulas

Module details#

`pystra.distributions`	Structural reliability marginals and distribution adapters.
`pystra.dependence.copula`	Continuous copula specifications, independent of physical marginals.
`pystra.dependence.joint`	Marginals plus a copula, and their isoprobabilistic transformations.
`pystra.dependence.transformation`	Normal Nataf coordinate transforms and directed Jacobians.
`pystra.dependence.correlation`	Correlation matrix handling and Nataf correlation modification.

Directed transformation derivatives#

Both Transformation and CopulaTransformation provide jacobian_u_wrt_x(u, x, marg) and jacobian_x_wrt_u(u, x, marg). The joint transformation already owns its marginals, so marg is optional there. Inputs are corresponding reference and physical points. Both matrices have shape (dimension, dimension) with output coordinates in rows and input coordinates in columns, in original model variable order. They are inverses at nonsingular points. standard_space identifies the reference law: normal Rosenblatt coordinates are independent; generalized Nataf with a Student-t copula has spherical, dependent Student-t coordinates.

Distribution reconstruction#

dist.parameters is a read-only constructor mapping; type(dist)(**dist.parameters) reconstructs the marginal. dist.with_parameters(**changes) returns an independent updated marginal, including its nested distributions. Native reconstruction parameters and sensitivity_params are separate: see Adding a distribution for moment updates, fixed bounds and custom subclass requirements.