| Abstract: |  Performing statistical hypothesis tests is an important method for analyzing real data sets occuring in various areas of the society. This thesis studies the properties of Zipf's law, its relationship to zeta distribution and the connection with heavy-tail phenomena occuring extensively in economics or demographics. Section 1 contains a short look
at the problem in question and also a brief historical explanation of the origins of Zipf's law. In section 2, properties of several related terms are described and a method of the performed analysis is introduced. A practical part of this work is in section 3 where the analysis is performed and results presented. Section 4 summarizes the results for both theoretical and empirical part of the document. Student's own contribution includes a consistent description of the theoretical part and also developing scripts for the analysis.
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