In the present thesis, robust statistical techniques are applied and developed for the economic problem of the analysis of personal income distributions and inequality measures. We follow the approach based on influence functions in order to develop robust estimators for the parametric models describing personal income distributions when the data are censored and when they are grouped. We also build a robust procedure for a test of choice between two models and analyse the robustness properties of goodness-of-fit tests. The link between economic and robustness properties is studied through the analysis of inequality measures. We begin our discussion by presenting the economic framework from which the statistical developments are made, namely the study of the personal income distribution and inequality measures. We then discuss the robust concepts that serve as basis for the following steps and compute optimal bounded-influence estimators for different personal income distribution models when the data are continuous and complete. In a third step, we study the case of censored data and propose a generalization of the EM algorithm with robust estimators. For grouped data, Hampel's theorem is extended in order to build optimally bounded-influence estimators for grouped data. We then focus on tests for model choice and develop a robust generalized Cox-type statistic. We also analyse the robustness properties of a wide class of goodness-of-fit statistics by computing their level influence functions. Finally, we study the robustness properties of inequality measures and relate our findings with some economic properties these measures should fulfil. Our motivation for the development of these new robust procedures comes from our interest in the field of income distribution and inequality measurement. However, it should be stressed that the new estimators and tests procedures we propose do not only apply in this particular field, but they can be used in or extended to any parametric problem in which density estimation, incomplete information, grouped or discrete data, model choice, goodness-of-fit, concentration index, is one of the key words.