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master's thesis
Uvod u teoriju ekstremnih vrijednosti
2023. urn:nbn:hr:166:351277
Vulin, Lea
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Vulin, L. (2023). Uvod u teoriju ekstremnih vrijednosti (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:351277

Vulin, Lea. "Uvod u teoriju ekstremnih vrijednosti." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:351277

Vulin, Lea. "Uvod u teoriju ekstremnih vrijednosti." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:351277

Vulin, L. (2023). 'Uvod u teoriju ekstremnih vrijednosti', Master's thesis, University of Split, Faculty of Science, accessed 11 May 2024, https://urn.nsk.hr/urn:nbn:hr:166:351277

Vulin L. Uvod u teoriju ekstremnih vrijednosti [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 May 11] Available at: https://urn.nsk.hr/urn:nbn:hr:166:351277

L. Vulin, "Uvod u teoriju ekstremnih vrijednosti", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:351277

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Metadata
TitleUvod u teoriju ekstremnih vrijednosti
Title (english)Introduction to extreme value theory
AuthorLea Vulin
MentorVesna Gotovac Đogaš (mentor)
Committee memberVesna Gotovac Đogaš (predsjednik povjerenstva)
Committee memberAna Laštre (član povjerenstva)
Committee memberMarcela Mandarić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-03-08, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Teorija ekstremnih vrijednosti elegantna je i matematički fascinantna teorija koja omogućuje raznoliku primjenu. U prvom dijelu rada cilj nam je pronaći graničnu distribuciju za maksimum nezavisnih i jednako distribuiranih slučajnih varijabli. Definiran je pojam maksimalne domene privlačnosti te klasa funkcija distribucije ekstremnih vrijednosti. Potom je dokazan Fisher i Tippett, Gnedenko teorem koji nam govori kako granične funkcije distribucije čine jednostavnu eksplicitnu jednoparametarsku familiju. U središnjem poglavlju rada predstavljen je prvi pristup domeni privlačnosti te je naveden von Misesov uvjet koji govori o dovoljnom uvjetu za pripadnost domeni privlačnosti. U završnom dijelu rada ustanovili smo nužne i dovoljne uvjete da bi funckija distribucije F pripadala domeni privlačnosti od Gγ.
Abstract (english)
Extreme value theory is an elegant and mathematically fascinating theory which ensures wide application. In the first part of the paper our interest is in finding possible limit distributions for sample maxima of independent and identically distributed random variables. Then the maximum domain of attraction and extreme value distributions were defined. Next Fisher and Tippett, Gnedenko theorem is proved and it tells us that the limit distribution functions form a simple explicit one-parameter family. In the central chapter of the paper the first approach to the domain of attraction is presented and von Mises condition was defined which state a sufficient condition for belonging to a domain of attraction. In the final part of the thesis we established necessary and sufficient conditions for a distribution function F to belong to the domain of attraction of Gγ.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:351277
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in statistics and computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2023-03-08 13:06:25