Using fractional derivatives to derive marginal densities
Methodology
2026-04-06 v3 Statistics Theory
Statistics Theory
Abstract
This paper presents a novel method for analytical derivations of marginal densities using the fractional derivatives of moment-generating functions. Although the method requires likelihood functions to take specific forms, its assumptions are otherwise modest. It only requires that the prior moment-generating functions exist, are finite, and are continuous and differentiable at certain points. We also present the probabilistic and statistical insights behind this method.
Cite
@article{arxiv.2409.11167,
title = {Using fractional derivatives to derive marginal densities},
author = {Si-Yang Li and David A. van Dyk and Maximilian Autenrieth},
journal= {arXiv preprint arXiv:2409.11167},
year = {2026}
}