Detail publikačního výsledku

Characteristic function and moment generating function of multivariate folded normal distribution

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

Originální název

Characteristic function and moment generating function of multivariate folded normal distribution

Anglický název

Characteristic function and moment generating function of multivariate folded normal distribution

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

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

Vydáno

10.05.2025

Nakladatel

Springer Nature

Místo

NEW YORK

ISSN

0932-5026

Periodikum

STATISTICAL PAPERS

Svazek

66

Číslo

4

Stát

Spolková republika Německo

Strany od

1

Strany do

23

Strany počet

23

URL

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

Plný text v Digitální knihovně

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="1--23",
  doi="10.1007/s00362-025-01711-z",
  issn="0932-5026",
  url="https://link.springer.com/article/10.1007/s00362-025-01711-z"
}

Dokumenty

s00362-025-01711-z