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Ocene parametrov večrazsežne normalne porazdelitve z metodo največjega verjetja
Munda, Jaka (Author), Peperko, Aljoša (Mentor) More about this mentor... This link opens in a new window

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Abstract
V diplomski nalogi obravnavamo primera podatkov z manjkajočimi podatki in primer brez manjkajočih podatkov, ki izhajajo iz zaporedja slučajnih vektorjev, ki so neodvisno enako porazdeljeni z večrazsežno normalno porazdelitvijo s parametroma vektorjem matematičnega upanja in kovariančno matriko. Za vsako obliko podatkov lahko po metodi največjega verjetja izračunamo cenilki parametrov porazdelitve. Pristopov za izračun cenilke po metodi največjega verjetja je več, v delu obravnavamo pristopa z matričnim odvajanjem in matrično transformacijo. Obravnavamo še monoton vzorec, ki je poseben primer manjkajočih podatkov, za katerega prav tako izračunamo cenilki za parametra po metodi največjega verjetja.

Language:Slovenian
Keywords:večrazsežna normalna porazdelitev, metoda največjega verjetja, matrično odvajanje, monoton vzorec
Work type:Bachelor thesis/paper (mb11)
Organization:FMF - Faculty of Mathematics and Physics
Year:2019
UDC:519.2
COBISS.SI-ID:18737497 Link is opened in a new window
Views:76
Downloads:46
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Secondary language

Language:English
Title:Maximum likelihood estimation of the parameters of a multivariate normal distribution
Abstract:
In this paper we consider sample with missing data and sample without missing data, that comes from multivariate normal distribution with parameters mean vector and covariance matrix. No matter the shape of the data we can estimate parameters with maximum likelihood estimation. There are various techniques for estimating parameters with maximum likelihood estimation. We consider two techniques, namely, matrix differentiation and matrix transformation. With both techniques we must derivate likelihood function that we get from the sample. We also consider monotone sample, which is a special case of missing data for which we can also estimate parameters with method of maximum likelihood estimation.

Keywords:multivariate normal distribution, maximum likelihood estimation, matrix differentiation, monotone sample

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