Solution to the practical problem of moments using non-classical orthogonal polynomials, with applications for probabilistic analysis

摘要

A method is presented for solving the "practical" problem of moments to produce probability density functions(PDFs)using non-classical orthogonal polynomials. PDFs are determined from given sets of moments by applying the Gram-Schmidt process with the aid of computer algebra. By selecting weighting functions of similar shape to desired PDFs, orthogonal polynomial series are obtained that are stable at high order and allow accurate approximation of tail probabilities.