A state-of-the-art statistical method with properties: Its utilization using the industrial investment funds and radiation data

Understanding fundamental demographic and environmental dynamics is crucial for accurate data analysis and prediction, particularly when confronting diverse geographical, economic, and physical challenges. In this context, we propose a state-of-the-art statistical model, specifically an improved family of estimators for the population distribution function, which incorporates auxiliary information to enhance estimation accuracy. This model leverages known distribution functions of auxiliary variables to construct efficient estimators for the distribution function of a target study variable. Building on established statistical techniques such as ratio, product, and classical regression estimators, our approach introduces refined alternatives that demonstrate superior statistical properties. These include reduced mean square error (MSE) and increased percentage relative efficiency (PRE) across a wide range of scenarios. Through theoretical justification and empirical validation, we show that our estimators consistently outperform traditional methods in terms of precision and robustness. To demonstrate the model’s versatility, we apply it to two complex, real-world datasets: industrial investment funds and environmental radiation data. In the financial domain, the model effectively captures trends and distributional characteristics critical to fund allocation and risk assessment. For environmental analysis, particularly radiation monitoring, the model identifies distributional shifts and anomalies, providing critical insights for ecological safety and policy-making. Our findings confirm that the proposed family of estimators constitutes a statistically powerful and adaptable modeling framework. It offers significant advancements in distribution function estimation and is well-suited for multidisciplinary applications that demand reliable inference under uncertainty. This research thus contributes to both the theory and application of modern statistical estimation in industrial and environmental sciences.