Characteristic function and moment generating function of multivariate folded normal distribution

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Characteristic function and moment generating function of multivariate folded normal distribution

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Characteristic function and moment generating function of multivariate folded normal distribution

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Statistical papers

ISSN

0932-5026

e-ISSN

1613-9798

Svazek periodika

66

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

23

Strana od-do

1-23

Kód UT WoS článku

001485555300002

EID výsledku v databázi Scopus

2-s2.0-105004668277