Distributions

Introduction

This module is used to define probability distributions. For computing polynomial Chaos expansions (see Polynomial Chaos Expansions), these will be input distributions into a forward model defining the stochastic variation of model parameters.

UncertainSCI currently supports the following types of random variables:

• Beta distributions (See BetaDistribution)

• Exponential distributions (See ExponentialDistribution)

• Normal distributions (See NormalDistribution)

• Discrete uniform distributions (See DiscreteUniformDistribution)

Tensorizations within a distribution are possible across these families by instantiating the distribution appropriately. Tensorizations across distributions is also possible, but requires individual instantiation of each distribution, followed by a constructor call to the TensorialDistribution class. (See TensorialDistribution)

E.g., a three-dimensional random variable \(Y = (Y_1, Y_2, Y_3)\) can have independent components, with the distribution of \(Y_1\) normal, that of \(Y_2\) beta, and that of \(Y_3\) exponential.

The distributions are located in the distributions.py file.