Publication detail

Characteristic function and moment generating function of multivariate folded normal distribution

BENKO, M. HÜBNEROVÁ, Z. WITKOVSKÝ, V.

Original Title

Characteristic function and moment generating function of multivariate folded normal distribution

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

Absolute value; Characteristic function; Folded normal distribution; Moment generating function; Multivariate normal distribution; Owen's normal integral

Authors

BENKO, M.; HÜBNEROVÁ, Z.; WITKOVSKÝ, V.

Released

10. 5. 2025

Publisher

Springer Nature

Location

NEW YORK

ISBN

0932-5026

Periodical

STATISTICAL PAPERS

Year of study

66

Number

4

State

Federal Republic of Germany

Pages from

1

Pages to

23

Pages count

23

URL

https://link.springer.com/article/10.1007/s00362-025-01711-z

Full text in the Digital Library

http://hdl.handle.net/11012/255198

BibTex

@article{BUT198334,
  author="Matej {Benko} and Zuzana {Hübnerová} and Viktor {Witkovský}",
  title="Characteristic function and moment generating function of multivariate folded normal distribution",
  journal="STATISTICAL PAPERS",
  year="2025",
  volume="66",
  number="4",
  pages="23",
  doi="10.1007/s00362-025-01711-z",
  issn="0932-5026",
  url="https://link.springer.com/article/10.1007/s00362-025-01711-z"
}