A Novel Sampling Method based on Orthogonal Polynomial Expansions and Applications

Abstract

We present a new method to sample random variables through the use of orthogonal polynomial expansions of the associated quantile function that utilize the inverse transform technique. In particular, we obtain an explicit representation of the quantile function through an orthogonal expansion using Legendre polynomials as a basis. This enables the sampling of a broad class of random variables directly through the inverse transform method, which are otherwise quite challenging or inefficient to sample with more traditional alternative techniques such as acceptance-rejection sampling. We illustrate the accuracy and efficiency of the new method through numerical examples and by comparing to benchmark cases in the literature.

Keywords: integral transform, inverse transform method, orthogonal polynomial, sampling

JEL Classification: C58, G12, G13, G14