Modeling Income Distributions Using Gamma and Lognormal Models: A Case Study from the University of Zakho

Income distribution modeling plays a critical role in understanding wage structures and inequality within public institutions, particularly in developing economies such as the Kurdistan Region of Iraq. This study examines the suitability of the Gamma and Lognormal distributions for modeling the income structure of university affiliates at the University of Zakho. A systematic sample of 250 employees was selected from the university’s total workforce. Two estimation techniques  Maximum Likelihood Estimation and the Method of Moments  were employed to estimate the parameters of both distributions. For the Gamma model, three numerical algorithms (Newton–Raphson, Broyden, and Bisection) were applied to solve the nonlinear likelihood equations, producing stable and consistent parameter estimates. Model adequacy was evaluated using multiple goodness-of-fit tests, including Chi-square, Kolmogorov–Smirnov, Anderson–Darling, and Cramér–von Mises statistics. The results revealed that both distributions adequately describe the total salary data, with MLE providing the best overall fit (e.g., p > 0.10 in K–S and A–D tests) and lower variability compared with MEM. Conversely, both models performed poorly for basic salarie, suggesting the need for more flexible or mixed-distribution approaches in such structured data. Overall, the findings confirm the empirical relevance of distributional choice and estimation strategy in modeling income data. The study provides quantitative evidence supporting the use of MLE-based Gamma and Lognormal models as effective tools for assessing income dispersion and inequality in higher-education institutions. 

Income distribution modeling plays a critical role in understanding wage structures and inequality within public institutions, particularly in developing economies such as the Kurdistan Region of Iraq. This study examines the suitability of the Gamma and Lognormal distributions for modeling the income structure of university affiliates at the University of Zakho. A systematic sample of 250 employees was selected from the university’s total workforce. Two estimation techniques  Maximum Likelihood Estimation and the Method of Moments  were employed to estimate the parameters of both distributions. For the Gamma model, three numerical algorithms (Newton–Raphson, Broyden, and Bisection) were applied to solve the nonlinear likelihood equations, producing stable and consistent parameter estimates. Model adequacy was evaluated using multiple goodness-of-fit tests, including Chi-square, Kolmogorov–Smirnov, Anderson–Darling, and Cramér–von Mises statistics. The results revealed that both distributions adequately describe the total salary data, with MLE providing the best overall fit (e.g., p > 0.10 in K–S and A–D tests) and lower variability compared with MEM. Conversely, both models performed poorly for basic salarie, suggesting the need for more flexible or mixed-distribution approaches in such structured data. Overall, the findings confirm the empirical relevance of distributional choice and estimation strategy in modeling income data. The study provides quantitative evidence supporting the use of MLE-based Gamma and Lognormal models as effective tools for assessing income dispersion and inequality in higher-education institutions.