A statistical framework for descriptive analytics of inflation-adjusted income disparities

Traditional income distribution models, such as the classical lognormal, often fail to capture upper-tail behavior, a limitation that becomes more evident during periods of inflation and structural economic change. These weaknesses can lead to an underestimation of top-income concentration and misrepresentation of inequality dynamics, creating a methodological gap in distributional analysis. To address this gap, this study introduces the Scale-Inflated Lognormal Distribution (SILD), a parametric extension of the lognormal model that incorporates an inflation-adjusted scale parameter to better represent upper-tail income behavior. Unlike the standard lognormal and other benchmarks such as the Generalized Beta of the Second Kind (GB2) and Gamma–Pareto mixtures, the SILD provides a more flexible yet analytically tractable framework for modeling income distributions under inflationary pressures. The model supports descriptive analytics by enabling precise estimation of inequality and inflation-sensitive income responses, with parameters estimated using Maximum Likelihood Estimation (MLE) and validated through extensive Monte Carlo (MC) simulations. Applied to Malaysian Household Income Survey (HIS) data from 2007 to 2022, the SILD consistently outperforms the standard lognormal, yielding lower Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values as well as smaller Root Mean Square Error (RMSE) and Mean Squared Error (MSE) statistics. These results confirm the model’s robustness and reliability in capturing upper-tail behavior and inequality dynamics. Notably, the SILD framework equips policymakers with sharper analytical tools for evaluating inequality, designing progressive taxation, and refining welfare programs in inflationary contexts. Nonetheless, the model’s current limitations include its assumption of a time-invariant variance parameter, reliance on Malaysian data, and exclusion of wealth and consumption dimensions. Future research should extend this framework across countries and integrate broader socioeconomic indicators to enhance its generalizability and policy relevance. • Develop a statistical model for descriptive analytics of household income data. • Capture inflation-adjusted income patterns across socioeconomic segments. • Estimate model parameters using simulation and likelihood-based methods. • Evaluate model fit and inequality metrics to support economic diagnostics. • Enable data-driven insights into income dynamics over multiple survey years.