In the analysis of income and wage size distributions statistical measures of concentration are often used. They usually become basic tools in the investigations concerning poverty and social welfare issues. They can also be helpful to analyze the efficiency of a tax policy or to measure the level of social stratification and polarization. Among many income inequality measures the Gini and Zenga coefficients are of greatest importance. Unfortunately the standard errors of these measures, being actually sample statistics, are rarely reported in practice. Estimators of many concentration coefficients are nonlinear functions of sample observations thus their standard errors cannot be obtained easily. The methods of variance estimation that can solve this problem include: various replication techniques as jackknife, bootstrap and BRR methods, Taylor expansion technique and some parametric procedures based on income distribution models. In the paper some estimation methods for Gini and Zenga concentration measures are presented together with their application to the analysis of income distributions in Poland. This effort was made to compare the NUTS1 regions in Poland from the point of view of income inequality. The basis for the calculations was individual data coming from the Household Budget Survey conducted by Polish Central Statistical Office in the years 2006-2008. The variance estimates were obtained by means of the bootstrap and the parametric approach based on the Dagum type-I model.