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master's thesis
Booleov model slučajnog skupa
2023. urn:nbn:hr:166:700856
Končurat, Paula
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Končurat, P. (2023). Booleov model slučajnog skupa (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:700856

Končurat, Paula. "Booleov model slučajnog skupa." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:700856

Končurat, Paula. "Booleov model slučajnog skupa." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:700856

Končurat, P. (2023). 'Booleov model slučajnog skupa', Master's thesis, University of Split, Faculty of Science, accessed 21 January 2025, https://urn.nsk.hr/urn:nbn:hr:166:700856

Končurat P. Booleov model slučajnog skupa [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2025 January 21] Available at: https://urn.nsk.hr/urn:nbn:hr:166:700856

P. Končurat, "Booleov model slučajnog skupa", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:700856

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Metadata
TitleBooleov model slučajnog skupa
Title (english)Boolean random set model
AuthorPaula Končurat
MentorVesna Gotovac Đogaš (mentor)
Committee memberVesna Gotovac Đogaš (predsjednik povjerenstva)
Committee memberGoran Erceg (član povjerenstva)
Committee memberMarcela Mandarić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U prvom poglavlju je dana definicija Booleovog modela te osnovne funkcije i svojstva koja opisuju takav model. Od velike su važnosti i funkcionali kapaciteta, kako za Booleov model, tako i općenito za sve slučajne zatvorene skupove. U radu smo proučavali svojstva Booleovog modela s različitim vrstima zrna, a posebice je bitan onaj model koji ima konveksna zrna. Takoder, Booleov model osnovni je model za perkolaciju kontinuuma. U središnjem dijelu rada proučavali smo pokrivenost i povezanost modela. Zadnje poglavlje vezano je za statistiku i simulacije ovoga modela, pri čemu je naglasak na metodama procjene parametara modela i testiranju pretpostavki modela.
Abstract (english)
In the first chapter we gave the definition of the Boolean model and the basic functions and properties that describe such a model. Capacity functionals are also of great importance, both for the Boolean model and, in general, for all random closed sets. In this thesis, we studied the properties of the Boolean model with different types of grains, and the model with convex grains is one of the most important example. Also, the Boolean model is the basic model for continuum percolation. In the central part of the thesis, we studied the coverage and connectivity of the model. The last chapter is related to the statistics and simulations of this model, where the emphasis is on methods of estimating model parameters and testing model assumptions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:700856
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 conditionsOpen access
Terms of useLicence Attribution 4.0 International (CC BY 4.0) icon
Created on2023-09-26 07:34:35