In almost all studies concerned with the distribution of financial data skewness and leptokurtosis will be measured by the third and the fourth standardized moments. Additionally, there is the problem of some severe outliers in the data. Therefore, skewness and leptokurtosis will be overestimated because the standardized moments are very sensitive with respect to these outliers as the investigation of the influence function of higher order standardized moments shows. In the literature concerned with adaptive and robust statistical methods there are alternative proposals for measuring skewness and kurtosis. These measures depend on means only defined on a part of the support of the considered distribution or on quantiles. Also for these measures the influence functions will be derived to discuss the influence of isolated outliers
