Characteristic function and moment generating function of multivariate folded normal distribution
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Date
2025-05-10
Authors
Benko, Matej
Hübnerová, Zuzana
Witkovský, Viktor
0009-0005-8311-6301Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
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Abstract
In this study, we derive the characteristic function of the multivariate folded normal distribution, a distribution that arises when the magnitudes-but not the signs-of a normally distributed random vector are of interest. The folded normal distribution is widely applicable across various fields. Thus, obtaining an analytical expression for its characteristic function is pivotal in understanding its fundamental properties. Moreover, this allows one to facilitate numerical evaluations of complex distributions involving linear combinations of absolute values of dependent normal variables. The derivation is based on a novel expression of the moment generating function, formulated using the cumulative distribution function of the multivariate normal distribution. To validate our findings, we present two examples using our MATLAB implementation. We compare the characteristic function for the sum of the absolute values of elements of a multivariate normal vector with the simulated empirical counterpart. Additionally, we derive the second mixed moment of the bivariate folded normal distribution from the moment generating function, demonstrating its agreement with known theoretical expressions.
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Citation
STATISTICAL PAPERS. 2025, vol. 66, issue 4, p. 1-23.
https://link.springer.com/article/10.1007/s00362-025-01711-z
https://link.springer.com/article/10.1007/s00362-025-01711-z
Document type
Peer-reviewed
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Published version
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Language of document
en