Dvodimenzionalna i višedimenzionalna normalna razdioba

undergraduate thesis

• Title (english): Twodimensional and Multidimensional normal distribution
• Author: Barbara Topolovec
• Mentor: Mario Krnić (mentor)
• Committee member: Mario Krnić (predsjednik povjerenstva)
• Committee member: Lenka Mihoković (član povjerenstva)
• Committee member: Anamari Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2020-07-03, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu prikazana su i izvedena najvažnija svojstva dvodimenzionalne i višedimenzionalne normalne razdiobe, te su ilustrirana kroz nekoliko računskih primjera, kao i grafičkim prikazom. Izvedena je funkcija gustoće vjerojatnosti za oba slučaja, a prikazan je i zapis pomoću karakteristične funkcije. Definiran je pojam jedinične normalne razdiobe i pokazana je veza između jedinične i opće normalne razdiobe. Određena su značenja svih parametara normalne razdiobe: očekivanja, disperzije, te kovarijacijske matrice. U radu se proučava i odnos varijabli u slučajnom vektoru, odnosno njihova zavisnost i koreliranost prikazana u kovarijacijskoj matrici.

Abstract (english)

This paper presents some of the most important properties of bivariate and multivariate normal distribution, which are also illustrated through several examples, as well as by graphic representation. The probability density function is derived for both cases, as well as the characteristic function. The concept of standard normal distribution is defined, and it is also shown how standard normal distribution and general normal distribution are linked. All the parameters of normal distribution are defined: mean, variance and covariance matrix. This paper also studies the relationship between variables of the random vector, i.e. their dependence and correlation.

• Keywords: slučajna varijabla; slučajni vektor; neprekinuta razdioba; funkcija gustoće; karakteristična funkcija; marginalna razdioba; uvjetna gustoća; očekivanje; disperzija; standardna devijacija; nezavisnost; korelacija; kovarijacijski moment; kovarijacijska matrica; Jacobijeva matrica; Jakobijan; determinanta matrice; inverz matrice
• Keywords (english): random variable; random vector; continuous distribution; density function; characteristic function; marginal distribution; conditional distribution; mean; variance; deviation; independence; correlation; covariance matrix; covariance; Jacobian matrix; Jacobian determinant; matrix determinant; inverse matrix
• Language: croatian
• URN:NBN: urn:nbn:hr:168:396993
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-01-14 10:09:46