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master's thesis
Modeli miješanih distribucija
2025. urn:nbn:hr:126:989373
Marković, Krešimir
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Marković, K. (2025). Modeli miješanih distribucija (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:989373

Marković, Krešimir. "Modeli miješanih distribucija." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2025. https://urn.nsk.hr/urn:nbn:hr:126:989373

Marković, Krešimir. "Modeli miješanih distribucija." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2025. https://urn.nsk.hr/urn:nbn:hr:126:989373

Marković, K. (2025). 'Modeli miješanih distribucija', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 22 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:989373

Marković K. Modeli miješanih distribucija [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2025 [cited 2025 April 22] Available at: https://urn.nsk.hr/urn:nbn:hr:126:989373

K. Marković, "Modeli miješanih distribucija", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2025. Available at: https://urn.nsk.hr/urn:nbn:hr:126:989373

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Metadata
TitleModeli miješanih distribucija
Title (english)Mixture Models
AuthorKrešimir Marković
MentorIvan Papić (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2025-04-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Ovaj diplomski rad istražuje teorijske osnove i praktične primjene modela miješanih distribucija, ključnog alata za analizu heterogenih podataka. Rad objašnjava osnovne koncepte, uključujući odredivost modela i algoritam maksimizacije očekivanja (EM), koji se koristi za procjenu parametara. Praktični dio obuhvaća analize različitih miješanih modela, uključujući model Gaussovih mješavina (GMM) i binomne modele, primijenjene na stvarnim i simuliranim podacima. Ilustrirane su primjene u biomedicini i ekonomiji, s naglaskom na interpretabilnost rezultata i izazove poput odabira broja komponenti. Zaključno, rad naglašava važnost miješanih distribucija u statističkom modeliranju te pruža smjernice za njihovu uspješnu primjenu u istraživačkom i praktičnom kontekstu
Abstract (english)
This thesis explores the theoretical foundations and practical applications of finite mixture models, which are essential tools for analyzing heterogeneous data. The study explains fundamental concepts, including model identifiability and the Expectation-Maximization (EM) algorithm used for parameter estimation. The practical section covers analyses of various mixture models, including Gaussian Mixture Models (GMM), binomial, and exponential models, applied to both real and simulated data. Applications in biomedicine and economics are illustrated, emphasizing the interpretability of results and challenges such as determining the number of components. In conclusion, this thesis highlights the importance of mixture distributions in statistical modeling and provides guidance for their effective use in research and practical contexts.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:989373
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2025-04-22 06:07:42