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Náhodné mozaiky a jejich statistická analýza / Random tessellations and their statistical analysis

Statistical aspects of random mosaics have not been heretofore given enough attention. This thesis deals with the derivation of estimators and statistical tests in a three-dimensional Poisson-Voronoi mosaic model. The first chapter compiles elementary results in the fields of point processes, random closed sets and particle processes. These are used in a second chapter to deduce geometric properties of random mosaics. The third chapter introduces the statistical research itself, estimators and model tests. Horvitz- Thompson estimator is introduced in order to correct statistics calculated on a reduced sample. Own results are tried in a computer simulation and compared to existing research in the last chapter. Mainly, the quality of estimators and the power of proposed tests is observed. 1

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:452721
Date January 2021
CreatorsVook, Peter
ContributorsPawlas, Zbyněk, Dvořák, Jiří
Source SetsCzech ETDs
LanguageSlovak
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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