
Birthday problem
Drápal, Lukáš ; Anděl, Jiří (advisor) ; Dostál, Petr (referee)
In the presented work we discuss the birthday problem with unlike probabilities. First, we introduce the concept of majorization of vectors, Schur convexity of functions and Bell polynomials. Using these concepts we show the results from papers [6] and [8]. We also discuss the paper [7] and we point out its error. Then we present a program in language R that is simulating the problem. We use this program to calculate the probability for the true birthday problem in the Czech Republic and the effect of leap years. Finally, we show some applications of the birthday problem, especially the true surname problem in Japan [8].


Multivariate extreme value models and their application in hydrology
Drápal, Lukáš ; Jarušková, Daniela (advisor) ; Hušková, Marie (referee)
Present thesis deals with the multivariate extreme value theory. First, concepts of modelling block maxima and threshold excesses in the univariate case are reviewed. In the multivariate setting the point process approach is chosen to model dependence. The dependence structure of multivariate extremes is provided by a spectral measure or an exponent function. Models for asymptotically dependent variables are provided. A construction principle from Ballani and Schlather (2011) is discussed. Based on this discussion the pairwise beta model introduced by Cooley et al. (2010) is modified to provide higher flexibility. Models are applied to data from nine hydrological stations from northern Moravia previously analysed by Jarušková (2009). Usage of the new pairwise beta model is justified as it brought a substantial improvement of loglikelihood. Models are also compared with Bayesian model selection introduced by Sabourin et al. (2013). Powered by TCPDF (www.tcpdf.org)


Birthday problem
Drápal, Lukáš ; Anděl, Jiří (advisor) ; Dostál, Petr (referee)
In the presented work we discuss the birthday problem with unlike probabilities. First, we introduce the concept of majorization of vectors, Schur convexity of functions and Bell polynomials. Using these concepts we show the results from papers [6] and [8]. We also discuss the paper [7] and we point out its error. Then we present a program in language R that is simulating the problem. We use this program to calculate the probability for the true birthday problem in the Czech Republic and the effect of leap years. Finally, we show some applications of the birthday problem, especially the true surname problem in Japan [8].
