Intelligent Approach to Discovering a New Functional Model Quantifying the Long-Tail Distribution of Online Markets

Actual sales data are valuable but often inaccessible. Thus, researchers and practitioners rely on sales–sales rank relationship models, such as the power-law distribution, to infer sales information. However, these models often poorly fit the sales distribution of online markets due to the long-tail phenomenon, creating a need for a more precise functional model. This paper proposes a novel model discovery framework, genetic programming with two-phase pruning (GPTP), which combines genetic programming with a newly developed two-phase pruning method to automatically learn a functional model relating sales to sales rank. Through analysis of sales data from both offline and online markets for 203,994 product items in 148 categories, we discover a new natural-power-law model that outperforms the traditional power-law model and provides a more accurate mathematical means of quantifying the long-tail distribution in online markets. The findings demonstrate that the proposed GPTP framework can intelligently learn the generalized knowledge underlying large business datasets and precisely determine the universal functional relationship model across multiple product categories in a white-box manner. The new model will enable researchers and practitioners to more accurately predict actual sales and explore various marketing issues.