PreprintarXiv licencearXiv
Absolute moments of GH distribution
Abstract
In this work, we focus on deriving the absolute moments of the general ized hyperbolic (GH) distribution via its mean-variance mixture structure. Conditioning on the GIG mixing variable reduces the problem to Gaussian moment calculations and known GIG power moments, avoiding direct integration with Bessel functions. The variance gamma (VG), normal inverse Gaussian (NIG), hyperbolic, Normal, and Student t distributions emerge as natural special or limiting cases of the generalized hyperbolic family. This approach offers a substantially simpler and more transparent derivation, facilitating both implementation and verification.
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BibTeX
@misc{yin2026absolute,
title = {{Absolute moments of GH distribution}},
author = {Chuancun Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14422},
eprint = {2610.14422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14422},
}
RIS
TY - UNPB
TI - Absolute moments of GH distribution
AU - Chuancun Yin
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.14422
UR - https://arxiv.org/abs/2610.14422
AB - In this work, we focus on deriving the absolute moments of the general ized hyperbolic (GH) distribution via its mean-variance mixture structure. Conditioning on the GIG mixing variable reduces the problem to Gaussian moment calculations and known GIG power moments, avoiding direct integration with Bessel functions. The variance gamma (VG), normal inverse Gaussian (NIG), hyperbolic, Normal, and Student t distributions emerge as natural special or limiting cases of the generalized hyperbolic family. This approach offers a substantially simpler and more transparent derivation, facilitating both implementation and verification.
ER -