ERADist probability distribution class

MATLAB and Python 3 classes for the convenient definition and use of (joint) random variables.

The random variables are defined marginally by their parameters, moments (mean and standard deviations) or through data fitting. The parametrization of the distributions follows the nomenclature used in the courses taught in our group, and is summarized in the included document.

To model joint distributions, the first option is that the user defines the marginal distributions and the correlation matrix. The Nataf transformation (Gaussian copula) is then used to construct the joint distribution. Alternatively, the joint distribution can be defined via a graphical model (aka Bayesian network) and the corresponding conditional distributions. The Rosenblatt transformation is then used to transform the random variables from their original outcome space (X-space) to a standard normal outcome space (U-space). 

Member functions of the Nataf and the Rosen classes include standard functions such as pdf, cdf, random, but also functions that transform samples from the X-space to the U-space and vice versa. The latter is a common operation in reliability analysis.

Download

ERA_Distribution_Classes.zip(MATLAB, v. 05/2023)

ERA_Distribution_Classes.zip (Python, v. 05/2023)

Requirements

MATLAB, incl. Statistical toolbox, ERADist and ERANataf probability distribution classes (optional: Deep Learning Toolbox)

Python 3, incl. numpy, scipy, matplotlib, ERADist and ERANataf probability distribution classes (optional autograd)