Characteristic function and moment generating function of multivariate folded normal distribution

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F26%3A0198334" target="_blank" >RIV/00216305:26210/26:0198334 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s00362-025-01711-z" target="_blank" >https://link.springer.com/article/10.1007/s00362-025-01711-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00362-025-01711-z" target="_blank" >10.1007/s00362-025-01711-z</a>

Result language

angličtina

Original language name

Characteristic function and moment generating function of multivariate folded normal distribution

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10103 - Statistics and probability

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Statistical papers

ISSN

0932-5026

e-ISSN

1613-9798

Volume of the periodical

66

Issue of the periodical within the volume

4

Country of publishing house

DE - GERMANY

Number of pages

23

Pages from-to

1-23

UT code for WoS article

001485555300002

EID of the result in the Scopus database

2-s2.0-105004668277