Dear UQLab Community,
I have been working with UQLab, and it has significantly simplified my work—thank you for this incredible tool! I have a query regarding the choice of orthonormal polynomials for a given marginal distribution in Polynomial Chaos Expansion (PCE).
Specifically, I am dealing with a problem involving five input random variables with the following marginal probability density functions: Gamma, Log-Normal, Gamma, Inverse Gaussian, and Weibull.
I wish to understand how the PCE framework selects the appropriate orthonormal polynomial basis for distributions like Inverse Gaussian and Weibull. Does the procedure involve transforming the non-standardized PDFs into the standard normal space using isoprobabilistic transformations and subsequently using Hermite polynomials? Alternatively, is the polynomial basis selected based on the original marginal distribution (in its non-standardized form), followed by isoprobabilistic transformations to facilitate the computations?
I hope I have articulated my question clearly, and I look forward to your insights on this.
Thank you in advance for your guidance.
Best regards,
Waris