Statistical Modeling of the Cobb–Douglas Production Function: A Multiple Linear Regression Approach in Presence of Stable Distribution Noise

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600572
B. D. Coulibaly, G. Chaibi, M. El Khomssi
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Abstract

In this work, we delved into advanced modeling of economic relationships using the Cobb–Douglas production function as a theoretical foundation. Our primary goal was to develop an innovative multiple linear regression model by introducing innovations based on the \(\alpha\)-stable distribution. By adapting the traditional multiple linear regression model, our approach incorporates the \(\alpha\)-stable distribution to better represent the complexity of relationships between economic variables. This modification enables a better fit for asymmetric distributions and scenarios where data exhibit heavy tails. To assess the performance of our model, we applied it to real financial data. This practical step allowed us to evaluate the effectiveness and predictive capability of our approach in a real-world context, thus offering fresh perspectives for financial data analysis.

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柯布-道格拉斯生产函数的统计建模:存在稳定分布噪声时的多元线性回归方法
摘要 在这项工作中,我们以柯布-道格拉斯生产函数为理论基础,深入研究了经济关系的高级建模。我们的主要目标是通过引入基于 \(α\)-stable 分布的创新,建立一个创新的多元线性回归模型。通过调整传统的多元线性回归模型,我们的方法纳入了(\α)-稳定分布,以更好地表示经济变量之间的复杂关系。这种修改能更好地拟合非对称分布和数据显示重尾的情况。为了评估模型的性能,我们将其应用于真实的金融数据。这一实际步骤使我们能够评估我们的方法在现实世界中的有效性和预测能力,从而为金融数据分析提供新的视角。
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CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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