Browsing Mathematics by Author "Stanojević, Jelena"
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Stanojević, Jelena (Beograd , 2015)[more][less]
Abstract: The main goal of the thesis is the development of a new suggested trans- form con¯dence intervals for the ratio of the variances of the two samples. Since now, the methods based on the F statistic have been suggested in the literature. However, the defect of that intervals is the huge sensitivity in re- lation with assumption of parameters distribution. Suggested statistic could be modi¯ed. Edgeworth expansion of the t-statistic has found the place in the thesis and based on that intervals have been compared. Also, on the base of the simulation it was point out that Johnsons transformation give better result in the sense of probability covering in regard to F interval and interval based on Halls transformation. Moreover, the con¯dence intervals for the mean and variances for the one and two sample problems have been considered in the dissertation. Especially, the problem of the di®erence of the proportions for the two samples, with the numerical results and data from the insurance. In addition, the existing methods for the estimation of the extreme value index and the high quantiles have been reviewed. Particularly, the direct simulation estimation of the quantile and probability covering of its deviation from the rights value, for Pareto and Gamma distributions, and also for general Pareto distribution have been discussed. The results were obtained by large deviation theory and their generalization on the topological spaces is stated. In this research, beside the probability theory and elemen- tary principles of the classical analysis, methods of the statistical theory and statistical conclusions have been applied. URI: http://hdl.handle.net/123456789/4261 Files in this item: 1
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