Statistické aplikace urnových modelů

Abstract

This work shows various applications of urn models in practice. First, basic properties of the occupancy distribution are derived together with its asymptotic approximation. This model is applied and generalized in the theory of database systems for records search from a given database. An application to random texts is mentioned, namely the computation of the expected number of missing and common words in random texts. There are presented exact formulas, their asymptotic approximations and the approximations via occupancy distribution. Then, some urn models, which are used in the randomized response theory for finding out respondents' answers to sensitive questions, are described. These models are compared according to their accuracy and respondents' goodwill to answer. Finally, two non-parametric tests of empty boxes are derived, one for the hypothesis whether a random sample comes from a given population and the second for the hypothesis whether two independent random samples come from the same population. The powers of these tests are compared with commonly used tests for these hypotheses.