Many populations encountered in practice are skewed to the right and contain a couple of values which are much larger than the bulk of the data. Using standard estimators to estimate for example the mean value of such a population is likely to result in a large variance. In this thesis we examine the possibility to use parametric models for the right tail of such a population to achieve estimators with a smaller mean squared error than the standard ones.

The thesis consists of two papers. In paper I we derive four different point estimators using a Pareto distribution to model the largest population values. The estimators can be seen as generalizations of a non-parametric winsorization approach.  We also consider confidence intervals based on these estimators paired with simple plug-in estimators of the corresponding variance. In a small design-based simulation study two of the estimators are shown to work well compared to the design unbiased expansion estimator, at least for point estimation.

In paper II we consider an estimator very similar to one of those suggested in paper I, and compare it to other point estimators motivated by a distributional assumption for the tail of the population. The aim is to make a coherent account of estimators of this type already existing in the literature and to compare their performance. The empirical results indicate that making use of parametric models to derive the form of point estimators can be a fruitful approach for a wide range of right-skewed populations especially for small samples.