Measuring Inequality of Income Distributions in Egypt: An Empirical Study Using Weighted and Non-parametric Methods

One of the foundational tasks in statistical analysis is the design and implementation of sample surveys, which involve sampling error that affects the reliability and precision of the resulting estimates. Measures such as totals and means are insufficient on their own without corresponding indicators of statistical precision, such as confidence intervals. As such, any analytical method applied to survey data must accommodate data weighting, which is essential for producing valid and interpretable estimates. Within the field of economic research, income inequality represents a key application where the use of weighted data is critical. In this context, we introduce a weighted inequality index designed to improve the robustness of inequality measurement. To enhance its analytical rigor, the proposed index is accompanied by a non-parametric, bootstrap-based algorithm, designed to facilitate comparative assessments and statistical significance testing across various population subgroups (e.g., regions, countries, gender). A major advantage of this approach lies in its flexibility; it is suitable for both normally and non-normally distributed data, thereby broadening its applicability to real-world datasets that often deviate from standard distributional assumptions. To demonstrate the empirical utility and comparative performance of the proposed methodology, we applied it to household income data obtained from the Central Agency for Public Mobilization and Statistics (CAPMAS), based on nationally representative income and expenditure surveys conducted in 2015 and 2018. The empirical findings revealed a general decline in the values of the proposed inequality index across most Egyptian governorates between 2015 and 2018, indicating a modest trend toward greater income equality. This downward shift may be indicative of the effects of socioeconomic reform measures and targeted development policies aimed at reducing regional disparities. The results validate the practical relevance of the proposed index as a reliable tool for evaluating income inequality in diverse socioeconomic contexts.