Air pollution is closely associated with the development of respiratory illness. The aim of the present study was to assess the relationship between long-term exposure to PM2.5, PM10, NO₂, and SO₂ pollution and the incidence of lung cancer in the squamous subtype in south-eastern Poland from the years 2004 to 2014. We collected data of 4237 patients with squamous cell lung cancer and the level of selected pollutants. To investigate the relationship between the level of concentrations of pollutants and the place of residence of patients with lung cancer in the squamous subtype, proprietary pollution maps were applied to the places of residence of patients. To analyze the data, the risk ratio was used as well as a number of statistical methods, i.e., the pollution model, inverse distance weighted interpolation, PCA, and ordered response model. Cancer in women and in men seems to depend in particular on the simultaneous inhalation of NO₂ and PM10 (variable NO₂PM10) and of NO₂ and SO₂ (variable NO₂ SO₂), respectively. Nitrogen dioxide exercises a synergistic leading effect, which once composed with the other elements it becomes more persistent in explaining higher odds in the appearance of cancers and could constitute the main cause of squamous cancer.

Power-law (PL) formalism is known to provide an appropriate framework for canonical modeling of nonlinear systems. We estimated three stochastically distinct models of constant elasticity of substitution (CES) class functions as non-linear inverse problem and showed that these PL related functions should have a closed form. The first model is related to an aggregator production function, the second to an aggregator utility function (the Armington) and the third to an aggregator technical transformation function. A q-generalization of K-L information divergence criterion function with a priori consistency constraints is proposed. Related inferential statistical indices are computed. The approach leads to robust estimation and to new findings about the true stochastic nature of this class of nonlinear—up until now—analytically intractable functions. Outputs from traditional econometric techniques (Shannon entropy, NLLS, GMM, ML) are also presented.

In an era of growing climate concerns and complex environmental policy challenges, novel approaches for accurate carbon emissions measurement are urgently needed. This article introduces an innovative approach for predicting carbon dioxide emissions by analyzing the interaction between energy consumption and production efficiency, measured through an entropy-to-marginal product ratio. Unlike conventional metrics such as Eurostat measurements or the Kaya identity, our framework establishes explicit connections to fundamental physical laws governing energy transformation while offering flexible elasticity parameters that capture non-linear relationships between efficiency improvements and emission reductions. The research combines theoretical modeling with empirical validation across ten European countries, demonstrating how the entropy-based methodology accounts for both production complexity and energy efficiency where traditional linear models fall short. Analysis reveals that energy-efficient countries demonstrate lower entropy maximization under stable conditions, indicating a direct relationship between operational efficiency and environmental impact. Although the model demonstrates strong predictive capabilities with an exceptional accuracy/information cost ratio, limitations exist in achieving accuracy in some country cases. This study concludes by evaluating these strengths and constraints, acknowledging the need for extended time series analysis and sector-specific applications, and providing clear directions for future research that bridge this promising theoretical contribution with practical environmental policy applications.