Moments by Integrating the Moment-Generating Function
Econometrics
2025-10-21 v4 Computational Finance
Computation
Abstract
We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central and non-central moments. The expressions are relatively simple integrals that involve the MGF, but do not require its derivatives. We label the new method CMGF because it uses a complex extension of the MGF and can be used to obtain complex moments. We illustrate the new method with three applications where the MGF is available in closed-form, while the corresponding densities and the derivatives of the MGF are either unavailable or very difficult to obtain.
Cite
@article{arxiv.2410.23587,
title = {Moments by Integrating the Moment-Generating Function},
author = {Peter Reinhard Hansen and Chen Tong},
journal= {arXiv preprint arXiv:2410.23587},
year = {2025}
}