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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Geometric distribution and its multivariate version
 Pavlovičová, Diana ; Hlubinka, Daniel (advisor) ; Pawlasová, Kateřina (referee)
In this work we will discuss the basics of a multivariate geometric distribution, especially its two-dimensional version. First of all, we establish a fundamental definition in which we consider two types of failures. Next, we compute some of its properties. We then focus on a different version of the two-dimensional case which we obtain by conditioning and for which we again compute its properties. We extend this approach to the case where we consider three types of failures. We further generalize the obtained results for the case of a multivariate negative binomial distribution. Lastly, we focus on the estimates of the parameters of the fundamental two-dimensional version of the multivariate geometric distribution and present a simple simulation in which we demonstrate the accuracy of the obtained estimates. 1
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Glivenko-Cantelli theorem and its generalization
 Pustějovský, Zdeněk ; Omelka, Marek (advisor) ; Pawlasová, Kateřina (referee)
In this thesis we look at Glivenko-Cantelli theorem and its generalization. Firstly we prove the classical version of this theorem with empirical ditribution function and as its corollary we show uniform convergence of sample quantiles to the actual ones. Next we give definition of bracketing number and prove generalized version of Glivenko-Cantelli theorem for function classes with finite bracketing number. Then we show how from the generalized version of the theorem follows the classical one not only for real random variables, but also for random vectors. Lastly we give examples of some Glivenko-Cantelli classes of functions. Throughout the work we also have applications of proven theorems in mind. 1
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