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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Point processes of objects with random lifetime
 Kulla, Filip ; Dvořák, Jiří (advisor) ; Beneš, Viktor (referee)
The thesis deals with point processes of objects with random lifetime. The form of the likelihood function of an observed spatial-temporal pattern with random lifetimes is derived, where the formula is subsequently generalised to the case of censored life- times. Moreover, some simple parametric models are introduced and conditions under which they are non-explosive are derived. In addition, aspects of our implementation of the algorithm which generates a realisation of a given spatial-temporal point process with random lifetimes and of the likelihood-based estimation are discussed. The thesis contains a simulation study in which the use of the (partial) likelihood on simulated data is demonstrated and properties of resulting estimates are discussed. Furthermore, it contains an application of the partial likelihood to the real data, where the question of interest is the spatial dynamics of propagation of an observed population of flowers. 1
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Two-sample Wilcoxon test in the presence of ties
 Kulla, Filip ; Omelka, Marek (advisor) ; Maciak, Matúš (referee)
This work is devoted to the Wilcoxon rank-sum test in the presence of ties. In this work, asymptotic distribution of the Wilcoxon test statistic in the presence of ties is derived using well-known results about U-statistics. With the aid of this result, a corrected test statistic for data containing ties is proposed. Furthermore, the thesis examines the relation between the derived correction and conditional variance of the test statistic (and conditional expectation). Finally, by means of simulation, the effect of the derived correction on the actual significance level is examined as the number of tied observations increases. 1
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