Polynomial chaos approximation

Several 1D probability distributions are approximated using the polynomial chaos expansion method

The main file 'PC_examples_1D.m' contains basic examples, in which several probability distributions are approximated using the polynomial chaos (PC) expansion. The key components of this method lie in the calculation of the orthogonal polynomials and the computation of the PC coefficients:
i). Functions to compute N-dimensional Hermite, Charlier and Jacobi polynomial are provided; extension to other types of orthogonal polynomials is straightforward.
ii). The PC coefficients are estimated using the projection method, where the integral is solved using a Gauss-Hermite quadrature. This step was only programmed for the case of 1D Hermite polynomials. Therefore, further extension to other types of orthogonal polynomials is required. An implementation of the regression method for the estimation of the PC coefficients can deal with this problem (hopefully, it will be included in a future version).