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Poisson Approximations
Klikáč, Jan ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
This bachelor thesis deals with the counting probability using Poisson distri- bution and shows new ways of approximating Poisson distribution. The first chapter summarizes the findings regarding the Poisson distribution, its definition and properties. It also show a limit transition from the binomial distribution to Poisson distibution and examples demonstrating the usage of this limit transition. Brun Sieve is introduced in the second chapter. It gives a new possibility of transiting to a Poisson distribution. Random variables, which we want to appro- ximate, no longer need to have binomial distribution. Instead the property of expected value is required. The second part of the chapter includes a practical demonstration of the usage of Brun Sieve. In the third chapter we estimate size of the error that we made when approxi- mating to Poisson distribution. There is also formulated Stein-Chen theorem for estimating the error of Poisson approximation and its version for a special case. Keywords: Poisson distribution, Brun Sieve, Stein-Chen theorem 1
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The comparison of knowledge of electromagnetic field theory for laymen and experts within the civil emergency preparedness
VESELÁ, Barbora
The thesis "Comparison of knowledge of electromagnetic field theory of the laity and experts in the context of civil emergency preparedness" to put three goals: 1. The formation of the structure of an electromagnetic field for experts. 2. The reaching of the comparison of knowledge among experts and laymen. 3. Statistical processing of the results. The author has set the following hypotheses: H1. Theoretical distribution of knowledge in a sample of the general public will have a normal distribution . H2. Theoretical distribution of knowledge in a sample of professional community will not have a normal distribution. H3. The comparison of knowledge among the experts and the laymen will lead to an alternative hypothesis. The thesis was based on the knowledge of the theory curricular process. On the basis of this theory was made up not only the structure of the electromagnetic field, but also the questionnaire. An important step in this thesis was the creating a model structure of electromagnetic field . The structure was based on an analysis of the scientific system - the system of educational programs in the field of civil protection.The same structure was applied to the general public. An important step was to compare the knowledge of protect the population from experts and laymen. This issue has not been investigated in detail and it did not compare the knowledge of laymen and experts in the studied physics. The idea came from the possibility of extraordinarily events where respondents can meet with electromagnetic fields and will need the relevant theoretical knowledge. The aim was to the statistical evaluate of the applied questionnaires. There were applied nonparametric and parametric testing as the verification methods. The theoretical division of knowledge of experts is supposed Poisson distribution, on the contrary, the theoretical division of the general public should have a normal distribution. There was also compared the difference between knowledge of laymen and professionals. The using of the statistical methods have been received and confirmed the hypothesis and the thesis goals were fulfilled.
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Model pro rozdíl dvou Poissonových veličin
Volf, Petr
When the discrete count data are analyzed, we are often facing the problems with insufficient flexibility of Poisson distribution. However, in many instances the variable of the interest is the difference of two count variables. For these cases, so called Skellam distribution is available, derived originally as the difference of two correlated Poissons. The model contains latent variables, which leads quite naturally to the use of Bayes approach and to data augmentation via the Markov Chain Monte Carlo generation.
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