This chapter addresses the parametric and nonparametric techniques used in distributional analysis, focusing on topics such as inequality, poverty, and the modeling of income distributions. While these statistical and econometric techniques may seem secondary to broader questions of inequality and economic justice, they are essential. Without quantitative data on income and welfare distributions, discussions on inequality and poverty would remain purely theoretical. Empirical evidence provides the necessary foundation for analyzing and addressing these issues in practice. Understanding how to effectively use data, despite its limitations, is crucial for informed discussions in welfare economics and for shaping sound policy. The statistical challenges in distributional analysis are as significant as the theoretical ones, ensuring that theories of inequality and social welfare have practical applications.