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Introduction to Order Statistics Theory
Hanuš, Antonín ; Kulich, Michal (advisor) ; Klebanov, Lev (referee)
This thesis deals with the theory of order statistics. Its aim is to summarize the basic knowledge concerning the distribution of the order statistics of random variables that are absolutely continuous with respect to the Lebesgue Measure and afterwards use those order statistics for some specific distributions. The first chapter describes the derivation of the density and distribution function of order statistics in several ways as well as dealing with some functions of order statistics and their conditional distribution. The second chapter is devoted to the moments of order statistics and formulae for their calculation and to the relations between them. In the conclusion the previous theoretical findings are applied to the uniform, exponential and normal distributions. 1
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Order statistics
Tělupil, Dominik ; Hlávka, Zdeněk (advisor) ; Jurečková, Jana (referee)
The aim of this work is to introduce general notions of theory of order statistics and the method of ranked set sampling (RSS). This statistical method is based on ranking of observed random variables which allows us to con- struct an unbiased estimator with lower variance than by using the method of sim- ple random sampling. In this work we will study estimators of the expected va- lue. Furthermore, we will investigate some properties of estimators based on RSS and some modifications of this method. The thesis contains a chapter about soft- ware simulations which verify the properties of estimators based on RSS. 1
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Thermodynamics of interacting brownian particles
Herčík, Michal ; Chvosta, Petr (advisor) ; Ryabov, Artem (referee)
The thesis comprises single-file diffusion in an external time-dependent potential, the diffusion of particles in narrow channel where particles can not pass each other. We discuss the role of order statistics solving the dynamics of the particles. We focus on application of perturbation theory on Fokker- Planck equation for the combined stochastic process of position and work. The calculation of the first and second moment of work for a set of particles analytically. The comparison of these results with results based on computer simulations of trajectories. Computer simulation of marginal PDF of work for left and right particle and simultaneous PDF for a set of two external driven particles. Powered by TCPDF (www.tcpdf.org)
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Introduction to Order Statistics Theory
Hanuš, Antonín ; Kulich, Michal (advisor) ; Klebanov, Lev (referee)
This thesis deals with the theory of order statistics. Its aim is to summarize the basic knowledge concerning the distribution of the order statistics of random variables that are absolutely continuous with respect to the Lebesgue Measure and afterwards use those order statistics for some specific distributions. The first chapter describes the derivation of the density and distribution function of order statistics in several ways as well as dealing with some functions of order statistics and their conditional distribution. The second chapter is devoted to the moments of order statistics and formulae for their calculation and to the relations between them. In the conclusion the previous theoretical findings are applied to the uniform, exponential and normal distributions. 1
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