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Abstract:
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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. |