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

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.