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Confidence intervals for differences and ratios of proportions
Krnáč, Ľuboš ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
The Bachelor thesis deals with the creation of confidence intervals for diffe- rence of parameters of two distributions. In the first part we consider the problem of making such confidence intervals for differences. Then we try to find sufficient conditions for MOVER, which leads to new, non-trivial confidence intervals for difference of parameters of two distributions. These confidence intervals have im- proved and desired properties. There are also examples of usage of MOVER, and possible difficulties. The third section contains graphs of coverage probabili- ties for different input intervals. These graphs are made to show different levels of achieved coverage probabilities for some input intervals, namely Clopper-Pearson, Wald, Wilson and logit. 1
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Confidence Intervals for Binomial Parameters
Rusá, Pavla ; Kulich, Michal (advisor) ; Maciak, Matúš (referee)
The Bachelor thesis deals with the construction of confidence intervals for the parameter of the Binomial distribution. In the first part of the thesis we deal with the relationship between hypotheses testing and confidence in- tervals. The methods mentioned in this thesis are based on this relationship. The next part is devoted to the Clopper-Pearson method and its possible improvements which were made by Sterne, Crow, Blyth and Still. The gra- phical approach of Schilling and Doi is also worth noticing. Afterwards we present the methods based on the Normal approximation, particularly the Wilson method and the Wald method. Finally, all the methods mentioned in this thesis are compared in terms of coverage probability. 1
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Interval estimates for binomial proportion
Borovský, Marko ; Zvára, Karel (advisor) ; Sečkárová, Vladimíra (referee)
The subject of this thesis is the point estimate and interval estimates of the binomial proportion. Interval estimation of the probability of success in a binomial distribution is one of the most basic and crucial problems in statistical practice. The thesis is divided into three chapters. The first chapter is about maximum- likelihood estimation for a binomial proportion. Futhermore, we will describe several methods of the construction of confidence intervals. In the end, we will compare all intervals in term of the actual coverage probability and expected length. 1
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